Quantum seaweed algebras and quantization of affine Cremmer-Gervais r-matrices

金融高质量发展研究的国内外文献综述1. 国外文献综述国外有大部分学者就金融发展与经济增长二者之间的关系进行了研究。

Panicos (1996)等探究了金融发展与经济增长的关系，他们对16个国家的时间序列数据进行研究，研究表明，在相当多的国家，经济增长系统性地导致金融发展，总的来说，金融发展和经济增长之间的关系是双向的[1]。

Simon (2004)等以中国为例进行研究金融开放与地理位置之间的关系，他们认为尽管信息的电子传输会大大减少由于距离而导致的金融信息获取受阻，但地理因素仍然为金融服务主要集中于北京等特定地区的关键性因素[2]。

Arjana (2007)等利用了宏观和行业数据，分析国际金融一体化与金融发展对欧洲经济增长的非线性影响，结果显示出具有显著的非线性效应，认为金融一体化可能不会对增长本身产生积极的影响，其影响取决于国家金融市场的发展、宏观经济的稳定和机构的质量[3]。

Matías (2007)等认为国内金融发展对贸易和资本流动开放的国家的增长影响要小于在两个方面都封闭的国家，在允许资本流动的情况下，非贸易部门的规模对于国内金融体系自由化的机会具有重要作用[4]。

在对金融发展的衡量标准方面，King与Levine(1993)认为金融发展质量的各种衡量标准与实际人均国内生产总值增长率、实物资本积累速度以及经济体使用实物资本的效率提高密切相关[5]。

Pagano(1993)认为金融市场的产生与发展是对“金融发展”概念的重点，要研究金融的发展对经济的增长影响是否存在，以及具体的影响是什么，必须要具体说明相关的特定金融市场[6]。

2. 国内文献综述目前有关金融高质量发展的研究主要分成三方面，学者对于金融高质量发展面临的问题的研究、学者对金融发展质量内涵的界定以及学者关于高质量发展的研究。

对于金融高质量发展面临的问题，诸多学者基于不同的角度进行了详细的讨论。

李伟（2019）提出标准化建设对于金融高质量发展的作用，并就我国金融标准化工作存在的问题提出见解[7]。

Quantum Mechanics and ApplicationsQuantum mechanics is a fundamental branch of physics that deals with the behavior of matter and energy at the atomic and subatomic levels. It is a framework for describing the behavior of particles that are too small to be observed directly and for predicting their interactions with one another and with their environment. As a field, quantum mechanics has led to many groundbreaking discoveries and has revolutionized our understanding of the physical world.In this article, we will explore some of the key concepts of quantum mechanics and their applications in modern technology.Wave-Particle DualityOne of the fundamental concepts of quantum mechanics is wave-particle duality. Simply put, this means that particles like electrons and photons can exhibit both wave-like and particle-like behavior, depending on how they are observed. This concept was first proposed by Louis de Broglie in 1924 and has since been confirmed through numerous experiments.One of the most famous experiments that demonstrates wave-particle duality is the double-slit experiment. In this experiment, a beam of electrons or photons is fired at a screen with two slits. Behind the screen, a detector records the pattern of interference that is created by the particles passing through the slits and interfering with each other. This pattern is characteristic of waves rather than particles and demonstrates the wave-like nature of the particles.Quantum SuperpositionAnother fundamental concept of quantum mechanics is quantum superposition. This refers to the ability of particles to exist in multiple states or locations simultaneously. This idea is often illustrated using the famous thought experiment of Schrödinger's cat, in which a cat is placed in a box with a vial of poison that will be released if a particular radioactive atom decays. According to the principles of quantum mechanics, until the boxis opened and the cat is observed, it is in a state of superposition, in which it is both alive and dead at the same time.Quantum superposition is key to the field of quantum computing, which is a new method of processing information that promises to be much faster than classical computing. In a quantum computer, data is stored in quantum bits, or qubits, which can exist in multiple states simultaneously. This allows quantum computers to perform certain calculations much more quickly than classical computers.Quantum EntanglementAnother key concept of quantum mechanics is quantum entanglement. This refers to the phenomenon in which two particles become correlated in such a way that the properties of one particle are dependent on the properties of the other, even when the particles are separated by large distances.Quantum entanglement is a key component of quantum cryptography, which is a method of secure communication that relies on the principles of quantum mechanics. In quantum cryptography, information is encoded using qubits, which are then transmitted over long distances. Because the qubits are entangled, any attempt to intercept or measure them will cause them to become disturbed, alerting the receiver to the presence of an eavesdropper.Applications of Quantum MechanicsThe concepts of quantum mechanics have led to many practical applications in modern technology. One of the most well-known applications is the laser, which uses the principles of quantum mechanics to produce a beam of coherent light.Another important application of quantum mechanics is in the field of medicine. For example, magnetic resonance imaging (MRI) uses the principles of quantum mechanics to produce detailed images of the inside of the body. In an MRI machine, the patient is exposed to a strong magnetic field, which causes the protons in their body to become aligned with the field. When a radio wave is then applied to the patient, the protons release energy, which is detected by the MRI machine and used to produce an image.ConclusionIn conclusion, quantum mechanics is a fundamental branch of physics that has revolutionized our understanding of the physical world. Its concepts of wave-particle duality, quantum superposition, and quantum entanglement have led to many practical applications in modern technology, from lasers to medicine. As our understanding of quantum mechanics continues to develop, it is likely that we will see even more exciting applications in the years to come.。

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文档下载后可定制修改，请根据实际需要进行调整和使用，谢谢!本店铺为大家提供各种类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by this editor. I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you! In addition, this shop provides you with various types of practical materials, such as educational essays, diary appreciation, sentence excerpts, ancient poems, classic articles, topic composition, work summary, word parsing, copy excerpts, other materials and so on, want to know different data formats and writing methods, please pay attention!荧光非闪烁IIVI族半导体核壳量子点的研究量子点技术是近年来研究的焦点之一，这种新型半导体材料拥有独特的光学、电学和物理学性质，广泛应用于生物医药、显示、照明和能源等领域。

This proves (7) and also implies that D is grouplike: ∆D = = =
c1 cn bn ...b1 an 1 ν −1 εa1 ...an ta c1 . . . t cn ⊗ t b1 . . . t bn ε c1 cn bn ...b1 −1 ν Dεc1 ⊗ t b1 . . . t bn ε D ⊗ D.
1
Introduction
FRT algebras A(R) were introduced in [6] as the associative C-algebras generated by 1 and ta b ; a, b = 1, . . . , n with relations
c d b b cd Rab cd t e t f = t d t c R ef ,
In the quotient A of A(R), one also finds D2 = 1 for the square of the q-determinant. Proof. By virtue of the relations (1) and the properties of the epsilon tensor, the element
b cd ta = g ab , ct dg
(3)
ቤተ መጻሕፍቲ ባይዱ
1
and the quotient A of A(R) by the ideal generated by this relation is then a Hopf algebra with obvious antipode. However, for mathematical reasons, one would like the quotient A also to be dual quasitriangular. This is the case if the fundamental representations ρ± descend to a representation of A, i.e. if they respect (3). It is easily seen that this requirement is satisfied iff

第十二届全国代数表示论会议专题报告内容主题一：Monomorphism categories with applications in algebra and geometry 参考文献：1.C.M.Ringel and M.Schmidmeier, Invariant Subspaces of Nilpotent Linear Operators. I.2. C.M.Ringel and M.Schmidmeier, The Auslander-Reiten Translation in Submodule Categories3. D.KUSSIN, H.LENZING,AND H.MELTZER, NILPOTENT OPERATORS AND WEIGHTED PROJECTIVE LINES，arXiv: 1002,3797v12. Xiaowu Chen, STABLE MONOMORPHISM CATEGORY OF FROBENIUS CATEGORY3. PU ZHANG, MONOMORPHISM CATEGORIES, COTILTING THEORY, AND GORENSTEIN -PROJECTIVE MODULES4. XIAO-WU CHEN AND H. KRAUSE, INTRODUCTION TO COHERENT SHEAVES ON WEIGHTED PROJECTIVE LINES主题二：Quantum cluster algebras参考文献：1. Arkady Berenstein and Andrei Zelevinsky, Quantum cluster algebras, Adv. Math. 195 (2005), no. 2, 405-455, arXiv:0404446v2.2。

Fan Qin, Quantum cluster variables via Serre polynomials,arXiv: 1004.4171.报告人：朱彬，徐帆，丁明主题三：Quiver Hecke algebras and categorification of quantum groups Abstract: This series includes 6 lectures which give a brief introduction to the quiver Hecke algebras introduced independently by Khovanov and Lauda [1] and Rouquier [2]. These algebras resemble affine Heck algebras in some aspects and carry a natural Z-grading.More precisely, to each graph without loops and multiple edges (with the set I of vertices) we can attach a family of algebras R(_) for _ 2 NI. Let K0(R(_)) denotethe Grothendieck group of finitely generated graded projective(_)-modules. The direct sum R() = X_2NIK0(R(_))admits a multiplication and a comultiplication given by induction and restriction functors. It turns out that R() is isomorphic to the positive part of the quantum enveloping algebra associated with . Most remarkably, Khovanov and Lauda formu-late a precise conjecture relating the representation theory of quiver Hecke algebras and the canonical bases of quantum enveloping algebras. For the simply laced types, the conjecture is proved by Varagnolo and Vasserot [3], exploiting Lusztig’s geometric approach to the canonical basis.Speakers: Bangming Deng, Bin Li, Jinkui Wan, Zhonghua Zhao References:1. M. Khovanov and A. Lauda, A diagrammatic approach to categorification of quantum groups I, Representation Theory 13 (2009), 309–347.2. R. Rouquier, 2-Kac-Moody algebras, arXiv:0812.5023.3. M. Varagnolo and E. Vasserot, Canonical bases and Khovanov–Lauda algebras, arXiv: 0901.3992.1。

八卦一下量子机器学习的历史人工智能和量子信息在讲量子机器学习之前我们先来八卦一下人工智能和量子信息。

1956，达特茅斯，十位大牛聚集于此，麦卡锡（John McCarthy）给这个活动起了个别出心裁的名字：“人工智能夏季研讨会”（Summer Research Project on Artificial Intelligence），现在被普遍认为是人工智能的起点。

AI的历史是非常曲折的，从符号派到联结派，从逻辑推理到统计学习，从经历70年代和80年代两次大规模的政府经费削减，到90年代开始提出神经网络，默默无闻直到2006年Hinton提出深层神经网络的层级预训练方法，从专注于算法到李飞飞引入ImageNet，大家开始注意到数据的重要性，大数据的土壤加上计算力的摩尔定律迎来了现在深度学习的火热。

量子信息的历史则更为悠久和艰难。

这一切都可以归结到1935年，爱因斯坦，波多尔斯基和罗森在“Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”一文中提出了EPR悖论，从而引出了量子纠缠这个概念。

回溯到更早一点，1927年第五次索尔维会议，世界上最主要的物理学家聚在一起讨论新近表述的量子理论。

会议上爱因斯坦和波尔起了争执，爱因斯坦用“上帝不会掷骰子”的观点来反对海森堡的不确定性原理，而玻尔反驳道，“爱因斯坦，不要告诉上帝怎么做”。

这一论战持续了很多年，伴随着量子力学的发展，直到爱因斯坦在1955年去世。

爱因斯坦直到去世也还一直坚持这个世界没有随机性这种东西，所有的物理规律都是确定性的，给定初态和演化规律，物理学家就能推算出任意时刻系统的状态。

而量子力学生来就伴随了不确定性，一只猫在没测量前可以同时“生”和'死'，不具备一个确定的状态，只有测量后这只猫才具备“生”和'死'其中的一种状态，至于具体是哪一种状态量子力学只能告诉我们每一种态的概率，给不出一个确定的结果。

1991 Mathematics Subject Classification. 18D20, 35A99, 58G99, 81R50, 58F07, 58A50, 35Q53. Key words and phrases. Hopf algebras, monoidal category, braidings, braided differential operators, braided differential forms and braided de Rham complexes, quantizations. Typeset by AMS-TEX 1
2
V.LYCHAGIN
As usual we introduce braided differential 1-forms Ω1 (A) as a representative object for the functor of braided derivations in new category with morphisms generated by braided differential operators of degree 0. Our construction of braided differential forms and the de Rham complex is based on the following two assumptions: (1) An algebra of braided differential forms should be a braided commutative algebra generated by the base algebra A and symmetric bimodule Ω1 (A),and (2) de Rham differential d should b

第40卷第4期海洋学报Vol. 40，No. 4 2018 年4 月H aiyang Xuebao April 2018谢旭丹，王静，储小青，等.南海中尺度涡温盐异常三维结构[11].海洋学报，2018,40(4):1 — 14，（1〇丨：10.3969/〗.丨沾11.0253-4193. 2018. 04. 001Xic Xudan,Wang Jing,Chu Xiaoqing, ct al. Three-dimensional thermohalinc anomaly structures of mcsoscalc eddies in the South China Sca[J]. Haiyang Xuebao,2018 >40(4.) ： 1 —14 , doi： 10. 3969/j.issn.0253-4 193. 2018. 04. 001南海中尺度涡温盐异常三维结构谢旭丹S王静储小青2，程旭华2(L.中..山大学地理科学与_规划学R:广东省城市化与.地理空M S拟重点囊验室.广东广州5«27_為2.中爾麟学院南海 海#研究所.热带海洋玮壤菌■震禽实验虜S广东.广州《.酚〇»'摘要：基f1394—2015年:海面高炭.异常数据，采用—d in g-职gl.5中尺度涡翁探蹲算涂儀别#脔海蒸围内共5 _S个戾气旋涡£A E)和.3: 792.个气旋涡（C B)，结合世界海洋数据集（W O D l3)及中爾耕学院 南海海參#魔所(S C S I〇>繼盐魏测数据集，爰腳基于变分法_客.观插值方逢，合.威了南海t南:海各区 域中尺度i的温盐异常三维结41。

结果表明，本文采取的推值方式能有效地获得涡旋三錐结#，垂向 尺度上也与前人研究结果较为一致。

在平均状态下，南海A E媪盐异常强度明显大于C E,A E正位温 身常主.修慧构深度约M Q m5斑C E仅在.326 m以燦維持满灤结构―者乘太位温署常坶辑现在次表层约抑m上下，A E边2.02°C，C E达一1._t：。

SIAM JOURNAL ON CONTROL AND OPTIMIZATION SIAM JOURNAL ON CONTROL AND OPTIMIZATION JOURNAL OF DIFFERENTIAL GEOMETRY Scandinavian Actuarial Journal Scandinavian Actuarial Journal Annals of Applied Statistics APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION NUMERICAL ALGORITHMS SIAM JOURNAL ON MATHEMATICAL ANALYSIS INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY MATHEMATICS AND COMPUTERS IN SIMULATION MATHEMATICS AND COMPUTERS IN SIMULATION MATHEMATICS AND COMPUTERS IN SIMULATION Communications in Mathematical Sciences ADVANCES IN COMPUTATIONAL MATHEMATICS BIT NUMERICAL MATHEMATICS BIT NUMERICAL MATHEMATICS COMPUTATIONAL OPTIMIZATION AND APPLICATIONS COMPUTATIONAL OPTIMIZATION AND APPLICATIONS JOURNAL OF GLOBAL OPTIMIZATION JOURNAL OF GLOBAL OPTIMIZATION COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS ADVANCES IN MATHEMATICS Extremes Extremes JOURNAL OF ALGEBRAIC GEOMETRY BERNOULLI Bulletin of Mathematical Sciences JOURNAL OF FUNCTIONAL ANALYSIS Selecta Mathematica-New Series Selecta Mathematica-New Series ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS INSURANCE MATHEMATICS & ECONOMICS INSURANCE MATHEMATICS & ECONOMICS APPLIED NUMERICAL MATHEMATICS JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS MATHEMATISCHE ANNALEN ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS Kinetic and Related Models Kinetic and Related Models JOURNAL OF CLASSIFICATION COMPUTATIONAL STATISTICS & DATA ANALYSIS COMPUTATIONAL STATISTICS & DATA ANALYSIS APPLIED MATHEMATICS AND OPTIMIZATION Journal of Dynamics and Differential En Applied Mathematics and Computational Science Communications in Applied Mathematics and Computational Science ANNALS OF PROBABILITY JOURNAL OF BUSINESS & ECONOMIC STATISTICS JOURNAL OF NONLINEAR SCIENCE JOURNAL OF NONLINEAR SCIENCE JOURNAL OF NONLINEAR SCIENCE PSYCHOMETRIKA INTERNATIONAL STATISTICAL REVIEW SIAM JOURNAL ON NUMERICAL ANALYSIS SIAM JOURNAL ON SCIENTIFIC COMPUTING NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS PROBABILITY THEORY AND RELATED FIELDS JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY INVERSE PROBLEMS INVERSE PROBLEMS NONLINEARITY NONLINEARITY STATISTICS AND COMPUTING STATISTICS AND COMPUTING ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE IMA JOURNAL OF NUMERICAL ANALYSIS STUDIES IN APPLIED MATHEMATICS JOURNAL OF SCIENTIFIC COMPUTING GEOMETRIC AND FUNCTIONAL ANALYSIS JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS Analysis and Applications Analysis and Applications ANNALS OF APPLIED PROBABILITY JOURNAL OF DIFFERENTIAL EQUATIONS MATHEMATICS OF COMPUTATION JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS Analysis & PDE Analysis & PDE CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK SIAM JOURNAL ON APPLIED MATHEMATICS JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS Advances in Calculus of Variations Advances in Calculus of Variations BIOMETRIKA BIOMETRIKA BIOMETRIKA Advances in Data Analysis and Classification JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Journal of the Institute of Mathematics of Jussieu CALCOLO CALCOLO

The future of computing QuantumcomputingQuantum computing is a revolutionary technology that has the potential to change the world as we know it. Unlike classical computing, which relies on bits to process information, quantum computing uses quantum bits, or qubits, which can exist in multiple states at once. This allows quantum computers to perform complex calculations at an unprecedented speed, making them ideal for solving problemsthat are currently beyond the capabilities of classical computers. The future of computing is undoubtedly quantum, and it has the potential to revolutionize industries ranging from healthcare and finance to cybersecurity and logistics. One of the most exciting prospects for quantum computing is its potential to revolutionize drug discovery and development. The ability of quantum computers to quickly and accurately simulate molecular interactions could drastically reduce the time and cost involved in bringing new drugs to market. This could lead to the development of more effective treatments for a wide range of diseases, ultimately improving the quality of life for millions of people around the world. Additionally, quantum computing could also have a significant impact on materials science, allowing researchers to design new materials with properties that were previously thought to be impossible. In the field of finance, quantum computing has the potential to revolutionize risk analysis and portfolio optimization. The ability of quantum computers to quickly analyze vast amounts of data could lead to more accurate predictions of market trends and risks, ultimately leading to more efficient and profitable investment strategies. Furthermore, quantum computing could also have a significant impact on cryptography and cybersecurity. Theability of quantum computers to quickly factor large numbers could render many of the encryption methods currently in use obsolete, leading to a need for new, quantum-resistant encryption methods. Despite the immense potential of quantum computing, there are still significant challenges that need to be overcome before it becomes a practical reality. One of the biggest challenges is the issue of qubit stability. Quantum systems are incredibly delicate and are easily disrupted by their environment, leading to errors in calculations. Researchers are currentlyworking on developing error correction techniques to address this issue, but it remains a significant hurdle to overcome. Additionally, the development of practical quantum algorithms for real-world problems is still in its early stages, and it will likely be many years before quantum computers are capable of outperforming classical computers in a wide range of applications. Another significant challenge is the issue of scalability. Current quantum computers are still relatively small, with only a few dozen qubits, and are far from being able to compete with the processing power of classical supercomputers. Scaling up quantum computers to the point where they can outperform classical computers in a wide range of applications will require significant advancements in both hardware and software. Additionally, the development of a quantum computing ecosystem, including the necessary infrastructure and tools, will be essential for the widespread adoption of quantum computing. Despite these challenges, the future of quantum computing is incredibly promising. Governments and private companies around the world are investing heavily in quantum computing research, recognizing its potential to revolutionize a wide range of industries. In the coming years, we can expect to see significant advancements in both the hardware and software of quantum computers, bringing us closer to the realization of practical quantum computing. As quantum computing continues to mature, it has the potential to revolutionize industries, solve some of the world's most complex problems, and fundamentally change the way we think about computing. The future of computing is quantum, and the possibilities are truly endless.。

湿量子计算Wet Quantum Computing湿量子计算Quantum computing, a field that promises to revolutionize our understanding of computation, has recently seen a new addition: wet quantum computing. This emerging technology harnesses the unique properties of biological systems to perform quantum computations. 量子计算，这个有望彻底改变我们对计算理解的领域，最近迎来了新的成员：湿量子计算。

这种新兴技术利用生物系统的独特属性来执行量子计算。

At the heart of wet quantum computing lies the intricate structure and behavior of biological molecules, particularly proteins and nucleic acids. These molecules, found within the cells of all living organisms, possess quantum mechanical properties that can be exploited for computational purposes.湿量子计算的核心在于生物分子，特别是蛋白质和核酸的复杂结构和行为。

这些分子存在于所有生物体的细胞中，具有可用于计算目的的量子机械属性。

One of the key advantages of wet quantum computing is its natural compatibility with biological systems. Unlike traditional quantum computers, which require specialized hardware and extreme conditions to maintain quantum coherence, wet quantum computing utilizes the inherent stability and functionality of biologicalmolecules.湿量子计算的一个主要优势在于它与生物系统的自然兼容性。

V i ⊗ W ⊗ V ⊗(k−2−i) ≃ V (ωk ) as Uq (sln )-modules.
In the case of Uq (sln ), the answer is given by W = span{vi ⊗ vi , vi ⊗ vj + qvj ⊗ vi (i > j )}. An important remark here is that W is identified with the image of the so-called ˇ (z ) acting on V ⊗ V at z = q 2 . R-matrix R ˇ (z ) = (1 − q 2 z ) R
k
V ≃ V (ωk )
as sln -modules.
Here V (ωk ) stands for the irreducible finite-dimensional representation with the k -th fundamental weight ωk as the highest weight. Let us now consider the quantized enveloping algebra Uq (sln ) in the sense of Drinfel’d and Jimbo. We also have the fundamental representation V (ωk ) for Uq (sln ). We would like to realize V (ωk ) as a wedge-like representation. Since the coproduct of the Hopf algebra Uq (sln ) is non-cocommutative, the construction n becomes a bit tricky. Let V = i=1 Q(q )vi be the vector representation of Uq (sln ). Our problem can be stated as follows. Find a suitable vector subspace W of V ⊗ V such that

1
Introduction
The non-standard quantum deformation of sl(2, R) ≃ so(2, 1) [1], here denoted Uz (sl(2, R)), has been the starting point in the obtention of non-standard quantum algebras in higher dimensions. In particular, by taking two copies of Uz (sl(2, R)) and applying the same procedure as in the standard (Drinfel’d–Jimbo) case [2], a quantum so(2, 2) algebra has been obtained in [3], while the corresponding deformation for so(3, 2) has been found in [4]. These quantum algebras have been realized as deformations of conformal algebras for the Minkowskian spacetime. Furthermore, by following either a contraction approach [3] or a deformation embedding method [5], non-standard quantum deformations for other Lie algebras have been deduced; amongst them it is remarkable the appearance of a non-standard quantum Poincar´ e

PHY4604,Introduction to Quantum MechanicsSyllabusFall2004•Instructor:Peter Hirschfeld,Professor of Physics with interests in superconductivity and low temperature physics.Office Hours:NPB2156,Wed.7th(1:55pm)Thursday7th(1:55pm);Appointments will gladly be scheduled for those students who cannot make official hours.•Text:D.Griffiths,Introduction to Quantum Mechanics,Prentice-Hall,2004.•Recommended Supplementary Texts:1.M.Horbatsch,Quantum Mechanics Using Maple,Springer Publishing,(NY),1995.2.R.P.Feynman,R.B.Leighton and M.Sands,The Feynman Lectures on Physics,California Institute ofTechnology,1966,VIII.•Other Useful Quantum Mechanics Texts:1.P.J.E.Peebles,Quantum Mechanics2.S.Gasiorowicz,Quantum Physics Wiley,1996.3.C.Cohen-Tanoudji,B.Diu,and lo¨e,Quantum Mechanics,Wiley,1977.4.A.Messiah,Quantum Mechanics,North-Holland,1961.5.R.Shankar,Principles of Quantum Mechanics,Plenum,1994.•Other References on Symbolic Manipulation Program Maple1.Essential Maple7by Robert M.Corless2.Introduction to Maple by Andre Heck•Course Description:An introduction to the quantum theory,as formulated in the1920’s and1930’s by Born,Bohr,Schr¨o dinger, Heisenberg,and others.First,we’ll discuss how quantum theory arose in the face of certain discrepancies between19th-century classical theory and experiment.Then,I’ll try to impart a set of mathematical tools needed to formulate problems in quantum mechanics,introducing methods of theoretical physics required to solve them as needed.Topics covered will range from the practical,like the basics of atomic spectroscopy,to the abstract,e.g.measurement theory and quantum“paradoxes”like Schr¨o dinger’s cat.For a more detailed set of topics see schedule below.I intend to stretch your mind.•Prerequisites:One year of general physics with calculus,or permission from a department undergraduate advisor is required. It is recommended–but not required–that before taking PHY4604,students take Physics C(Modern Physics) complete the calculus sequence,and have had some exposure to ordinary differential and partial differential equations,as well as matrix/linear algebra.1•Required Work:Homework:The weekly problem sets represent by far the most important element of the course,and where you will learn the most.I encourage you to work on them in groups if you like;the problems will occasionally be difficult and may require more than one head!However,be convinced in the depths of your soul that letting others do the work for you will lead to disaster at test time.A good technique for many students is to try all the problems individually,then get together in a group for the tough ones.Problem sets will be posted on the web every Monday,and be due the following Monday.Some(not all)will contain problems which are to be solved using Maple(see below).Each problem set will be worth a total of 10points,and your grade will decay4points for thefirst day it is late after the solutions are posted,plus a further1/2point for each subsequent week.I will drop the lowest two homework grades at the end of the course.My goal will be to hand the problem sets back Monday one week after receiving them,but occasionally other considerations will interfere,and I ask for your understanding.Tests:There will be three required tests and afinal examination administered in class on the following dates:In-class test1NPB1101,Fri.,Oct.8In-class test2NPB1101,Fri.,Nov.5In-class test3NPB1101,Fri.,Dec.3Final NPB1101,Time TBA,Dec.16You must bring writing instruments and a student identification card with a photo for all tests and thefinal. All necessary paper will be provided,and calculators will not be allowed or needed.The lowest absolute score of the3tests will be dropped.Due to this policy,no makeup tests will be allowed. Makeup policy:Since the policy of dropping tests and homeworks is very generous,no makeups are allowed. Grading Policy:The various components of yourfinal grade will be weighted as follows:Tests1-340%Final20%Homework40%There will be no“extra credit”under any circumstances.Letter grades will be assigned according to a”curved”distribution.However,the following minimum scores will guarantee the following grades:85-A,80-B+,72-B,65-C+,60-C,55-D+,50-D.For example,depending on the”curve”,a score of72%may be sufficient for a B+.Your actual raw percentage score should not be compared to those you receive in other courses.Because physics involves very different kinds of skills from other science and mathematics courses,even very good students will generally not solve all parts of most problems correctly.Demonstrating that you understand a problem even if you cannot solve all its parts will result in partial credit.If you feel your test has been unfairly or improperly graded,you are welcome to present your test booklet for regrading.However,the entire exam is then subject to regrading,and thefinal grade may be lower!You2PHY4604--Course Schedule Fall 2004Week Topic(s) ReadingHomeworkNotesAug. 23 Dilemmas of classical physics• Energy quantization• Boltzmann distribution• Energy of harmonic oscillator• Equipartition• Specific heat of solids• Blackbody radiationPH Notes None DilemmasAug. 30 Quantization of normal modes• Wave equation• Normal modes of cavity• Periodic boundary conditions• Counting modes• Planck lawNotesProb. Set 1due Sept. 10BlackbodySept. 6 Monday Sept. 6 is Labor Day Other early evidence for quantum behavior• Photoelectric effect• Ritz principle• Bohr model• Motion of wave packet• Electrons as wavesNotesProb. Set 2due Sept. 15OtherevidenceSept. 13 Schrödinger equation I• Dynamics of Schrödinger’s ψ-fctn.• Spherically symmetric potential (H-atom)• 1D simple harmonic oscillator• Particle in electromagnetic fieldNotes,Chs. 1, 2Prob. Set 3due Sept. 22SchroedingerISept. 20 Schrödinger equation II• Probabilistic interpretation of ψ-fctn.• Fourier transform• Measuring a particle’s momentum• Uncertainty principleNotes,Ch. 1,2Prob. Set 4due Sept. 29SchroedingerIISept. 27 Operator formalism I• Momentum operator• Expectation values• Inner products• Hermitian adjoint• Eigenstates and eigenvaluesNotes,Ch. 3OperatorIOct. 4 Operator Formalism II• Completeness• Measurement• ParityNotes,Ch. 3Prob. Set 5due Oct. 11Operator IIFriday, Oct. 8 Test 1 on 1st6 weeks - - -Oct. 18 Hilbert space and matrix mechanics• Dirac’s bra and ket notation• Postulates and probability• Position representationNotes,Ch. 3Prob. Set 6due Oct. 18HilbertIOct. 25 Angular Momentum I• Orbital angular momentumoperators• L-eigenvalues from ladderoperators• Eigenvalues from Schr\"odingerEqn• Commutation rels. -- sphericalpotential• L generates rotationsNotes,Ch. 4None AMINov. 1 Angular momentum II• Central forces & pseudopotential• H-atom bound states• QM 2-body problem• Reduction to 1-body problemNotes,Ch. 4Prob. Set 7due Nov. 1AMIIFriday Nov. 5 Test 2 on next 4 weeks- -Nov. 8No classNov. 12 (Homecoming) Spin I• Electron spin• Pauli spin matrices• 2 spin-1/2 particles• Many particles• Electron magnetic moment, precessionNotes,Chs. 4,5Prob. Set. 8due Nov. 8SpinINov. 15 Spin II• Absprption• Resonant scattering• t-matrixNotes,Chs. 4,5Prob. Set 9due Nov. 15SpinIINov. 22 No class Wed.or Friday (Thanksgiving) Measurement I• Superposition• Collapse of wave function• Role of observer- NoneMeasurementNov. 29 Measurement II• Superposition• Collapse of wave function-Prob. Set 10due Nov. 29Friday Dec. 3 Test 3 on spin - - - Dec. 6 Review - NoneDec. 16 Final exam (comprehensive)。

量子科技展览内容提纲范文Quantum technology exhibition is an exciting opportunity to showcase the latest advancements in the field. 量子科技展是展示该领域最新进展的绝佳机会。

Visitors to the exhibition can expect to learn about the cutting-edge research and practical applications of quantum technology. 参观者们可以期待了解关于量子科技尖端研究和实际应用的内容。

One of the key highlights of the exhibition will be the demonstrations of quantum computing, which has the potential to revolutionize the way we process information. 展览的一个重要亮点将是量子计算的演示，它有可能彻底改变我们处理信息的方式。

In addition to computing, quantum technology also has applications in quantum communication, quantum sensing, and quantum cryptography. 除了计算，量子技术还在量子通信、量子传感和量子密码学方面具有应用。

Visitors can explore the interactive exhibits and engage with expertsin the field to gain a deeper understanding of the potential impact of quantum technology on various industries. 参观者们可以探索互动展品，并与该领域的专家交流，以更深入地了解量子技术对各行业潜在影响。

a rXiv:h ep-th/975235v129M a y1997Quanta without quantization James T.Wheeler Department of Physics,Utah State University,Logan,UT 84322Abstract The dimensional properties of fields in classical general relativity lead to a tangent tower structure which gives rise directly to quantum mechanical and quantum field theory structures without quantization.We derive all of the fundamental elements of quantum mechanics from the tangent tower structure,including fundamental commuta-tion relations,a Hilbert space of pure and mixed states,measurable expectation values,Schr¨o dinger time evolution,“collapse”of a state and the probability interpretation.The most central elements of string theory also follow,including an operator valued mode expansion like that in string theory as well as the Virasoro algebra with central charges.Introduction The detailed structure of quantum systems follows by fully developing the scaling structure of spacetime.Thus quantum systems -de-spite their Hilbert space of states,operator-valued observables,interferingcomplex quantities,and probabilities -are rendered in terms of classical spacetime variables which simultaneously form a Lie algebra of operators on the space of conformal weights.This remarkable result follows from the tangent tower structure implicit in general relativity.We develop this structure,cite a central theorem,then examine some properties of tensors over the tangent tower.Finally,we apply these ideas to quantum mechanics and string theory,showing how the core elements of both arise classically.1The weight tower and weight maps Consider a spacetime(M,g)with dynamicalfields,{ΦA|A∈A}of various conformal weights and tensorial types.Under a global change of units byλ,letΦA→(λ)w AΦA(1) where w A is called the conformal weight ofΦA.Normally,physicists simply insert these scale factors by hand when needed,without mentioning the im-plicit mathematical structures their use requires,but these structures turn out to be interesting and important.The tower structure begins with the set of conformal weights,W≡{w A| A∈A},which must be closed under addition of any two different elements. Possible sets include the reals R,the rationals Q,the integers J,and the finite set{0,1,−1}.For most physical problems we can choose the unit-weight objects to give W=J.Next,define the equivalence relationΦA∼=ΦB if w A=w B and∃ηsuch thatΦA=ηΦB(2) which partitions the tangent space T M into a tower of projective Minkowski spaces,P M,one copy for each n∈J=W.This partition enlarges the linear transformation group of the tangent space into the direct product of the Lorentz group and the group of weight maps.While the Lorentz trans-formations have their usual effect,general weight maps act on conformal weight.To see that the group is a direct product,consider the product of an n-weight scalarfield with an m-weight vectorfield.Since the linear trans-formations preserve the Lorentz inner product between arbitrarily weighted vectors,the resulting(n+m)-weight vectorfield remains parallel to the orig-inal m-weight vectorfield under Lorentz transformation.Therefore,Lorentz transformations map different weight vectors in the same way.We now investigate weight maps.Just as the only measurable Lorentz objects are scalars,the only measurable tangent tower quantities are zero weight scalars1.Therefore,to readily form zero weight scalars,we classify weight maps and tensors over W by their conformal weights.The generator of global scale changes,D,determines the weights offields according to2DΦA=w AΦA(3)while the generators Mαof definite-weight maps satisfy[D,Mα]=nαMα(4) where nα∈J.Then Mαmaps n-weightfields to(n+nα)-weightfields,making the construction of0-weight quantities straightforward.The following theorem now holds[1]:Theorem.Let V be a maximally non-commuting Lie algebra consisting of exactly one weight map of each conformal weight.Then V is the Virasoro algebra with central charge,[M(m),M(n)]=(m−n)M(m+n)+cm(m2−1)δ0m+n1(5) The lengthy proof relies on explicit construction through a series of induc-tive arguments.It is highly significant to note that the real-projective tangent tower produces the same central charge for V as unitarily-projective string theory,despite its classical character.This is thefirst concrete evidence that some phenomena widely regarded as“quantum”can be understood from a classical standpoint.Tensors over the weight tower Having understood the algebraic char-acter of definite-weight weight maps,we next look at the tensors they act on.Since Lorentz transformations decouple from weight maps,the Lorentz and conformal ranks are independent.ThusT a1···a rn1···n s:(P M)r⊗J s→R(6) is a typical rank(r,s)tensor.Weight maps act linearly on each label n i.Particularly relevant to quantum systems are(0,1)tensors.Withηk a k-weight scalar,Dηk=kηk,a general(0,1)tensor is an indefinite-weightlinear combinationΦ=∞k=−∞φkηk(7)We immediately see the need for some convergence criterion.Imposing a norm provides such a criterion,and with a norm these objects form a Hilbert space,H.The simplest norm uses a continuous representation for the(0,1)tensors defined byΦ(x)≡∞n=−∞φn e inx.(8) 3Clearly,Φ(x)exists only under appropriate convergence conditions,provided by including as the(0,1)tensors those vectors satisfying1δ(x−y)+c1(11)∂xfor D andM(k)(x,y)=e ikx(−i∂x−k)δ(x−y)(12) for the k-weight Virasoro operator.In eq.(11),D(x,y)requires the central distribution c to cancel surface terms from the product integral.Such terms are an artifact of the continuous representation.Physical effects of the tangent tower Now we describe physical effects of the tangent tower.We replace the usual(r,0)tensors of quantum mechan-ics and quantumfield theory by(r,1)or(r,2)tensors.In the remaining two sections we do this in detail for quantum mechanics,then briefly for string theory.Conformal weight and quantum mechanics The tangent tower under-pinning of all axiomatic features of quantum mechanics now follows imme-diately:commutation relations of operator-valued position and momentum vectors,a Hilbert space of pure and mixed states,measurable expectation values,Schr¨o dinger time evolution,“collapse”of a state and the probability interpretation.First,consider canonical commutators.Since w x=1and w p/h=−1, canonical coordinates lie in the subalgebra determined by W0={0,1,−1}⊂W.We temporarily consider operators in this subspace,replacing symplectic coordinates Q A=(q i,πj)by weight-map-valued6-vectorsˆQ A=(ˆq i,ˆπj)∈T a nm forming the Lie algebra[ˆQ A,ˆQ B]=c AB1(13)4where projective representation allows arbitrary central charges c AB.The only invariant antisymmetric symplectic tensor is the symplectic2-formΩAB= 0−δi jδj i0 (14)so we set[ˆQ A,ˆQ B]=ΩAB1(15) Furthermore,the natural symplectic metricK AB= 0δi jδj i0 (16)may be diagonalized by a symplectic transformation to new variablesˆR A= (ˆX i,ˆP j)such that˜K AB= δij−δij (17) or equivalentlyˆR′A=(ˆX i,iˆP j)with˜K′AB= δijδij (18)The zero signature of the symplectic metric requires an imaginary unit in relatingˆR′A toˆP j because the physicalˆX i andˆP j have the same metric, +δij.The projective algebra ofˆX i andˆP j is the canonical one[ˆX i,ˆP j]=iδij1(19)[ˆX i,ˆX j]=[ˆP i,ˆP j]=0(20) Thus,“quantum”(ˆX i,ˆP j)commutators follow from classical scaling consid-erations by replacing classical variables with weight tower operators in the {0,1,−1}subalgebra,and using the natural symplectic structure.Other quantum structures follow easily.Thus,definite weight scalars replace pure quantum states,while indefinite weight objects such asΦ(x)∈H replace mixed states.The construction of expectation values is simply a rule to generate a0-weight scalar.The rule works by matching elements of5H with their complex conjugates but the definition ofΦ(x)above translates this into the manifestly0-weight sumΦ,Ψ =1dτinflat spacetime while uµWµΦgives the action ofa weight map H≡uµWµon the weight superpositionΦ(xν;x).Identifying H as the Hamiltonian operator[2],eq.(22)becomes the Schr¨o dinger equation. The free-particle form for H is the zero-weight quantityH= dˆX jL ,L2φ−2,etc.,with L some standard unitof length.Therefore the rules of quantum mechanics have natural classical interpre-tations in terms of the scale-invariance properties of spacetime.6Conformal weight and quantumfield theory Just asfield theory emerges as the limiting case of multiparticle dynamics,and quantumfield theory emerges as a blend of quantum mechanics and special relativity[3], we can imagine retracing the preceding arguments to derive the principles of quantumfield theory.After all,the quantum state is afield,even in quantum mechanics.Thus,we may anticipate a classical tangent tower in-terpretation of quantumfield theory.As striking as this conjecture seems, we now demonstrate a more striking claim:the tangent tower contains the essential elements of string theory[4].Minor manipulations of a definite weight(1,2)tensorαµ(k)(x,y)found bywriting theδ-function in D asδ(x−y)=1References[1]Wheeler,J.T.,String without strings,in preparation.[2]Wheeler,J.T.,Phys.Rev.D44(1990);Wheeler,J.T,Proceedings ofthe Seventh Marcel Grossman Meeting on General Relativity,R.T.Jantzen and G.M.Keiser,editors,World Scientific,London(1996)pp 457-459.[3]Weinberg,S.,The quantum theory offields,Cambridge University Press(1995).[4]Green,M.B.,J.H.Schwarz and E.Witten,Superstring theory,Cam-bridge University Press(1987).[5]Kuchar,K.V.and C.G.Torre,J.Math.Phys.30(8),August1989.8。

Ultra-High Efficiency Photovoltaic Cells for Large Scale Solar Power GenerationYoshiaki NakanoAbstract The primary targets of our project are to dras-tically improve the photovoltaic conversion efficiency and to develop new energy storage and delivery technologies. Our approach to obtain an efficiency over40%starts from the improvement of III–V multi-junction solar cells by introducing a novel material for each cell realizing an ideal combination of bandgaps and lattice-matching.Further improvement incorporates quantum structures such as stacked quantum wells and quantum dots,which allow higher degree of freedom in the design of the bandgap and the lattice strain.Highly controlled arrangement of either quantum dots or quantum wells permits the coupling of the wavefunctions,and thus forms intermediate bands in the bandgap of a host material,which allows multiple photon absorption theoretically leading to a conversion efficiency exceeding50%.In addition to such improvements, microfabrication technology for the integrated high-effi-ciency cells and the development of novel material systems that realizes high efficiency and low cost at the same time are investigated.Keywords Multi-junctionÁQuantum wellÁConcentratorÁPhotovoltaicINTRODUCTIONLarge-scale photovoltaic(PV)power generation systems, that achieve an ultra-high efficiency of40%or higher under high concentration,are in the spotlight as a new technology to ease drastically the energy problems.Mul-tiple junction(or tandem)solar cells that use epitaxial crystals of III–V compound semiconductors take on the active role for photoelectric energy conversion in such PV power generation systems.Because these solar cells operate under a sunlight concentration of5009to10009, the cost of cells that use the epitaxial crystal does not pose much of a problem.In concentrator PV,the increased cost for a cell is compensated by less costly focusing optics. The photons shining down on earth from the sun have a wide range of energy distribution,from the visible region to the infrared region,as shown in Fig.1.Multi-junction solar cells,which are laminated with multilayers of p–n junctions configured by using materials with different band gaps,show promise in absorbing as much of these photons as possible,and converting the photon energy into elec-tricity with minimum loss to obtain high voltage.Among the various types of multi-junction solar cells,indium gallium phosphide(InGaP)/gallium arsenide(GaAs)/ger-manium(Ge)triple-junction cells that make full use of the relationship between band gaps and diverse lattice con-stants offered by compound semiconductors have the advantage of high conversion efficiency because of their high-quality single crystal with a uniform-size crystal lat-tice.So far,a conversion efficiency exceeding41%under conditions where sunlight is concentrated to an intensity of approximately5009has been reported.The tunnel junction with a function equivalent to elec-trodes is inserted between different materials.The positive holes accumulated in the p layer and the electrons in the adjacent n layer will be recombined and eliminated in the tunnel junction.Therefore,three p–n junctions consisting of InGaP,GaAs,and Ge will become connected in series. The upper limit of the electric current is set by the mini-mum value of photonflux absorbed by a single cell.On the other hand,the sum of voltages of three cells make up the voltage.As shown in Fig.1,photons that can be captured in the GaAs middle cell have a smallflux because of the band gap of each material.As a result,the electric currentoutputAMBIO2012,41(Supplement2):125–131 DOI10.1007/s13280-012-0267-4from the GaAs cell theoretically becomes smaller than that of the others and determines the electric current output of the entire tandem cell.To develop a higher efficiency tandem cell,it is necessary to use a material with a band gap narrower than that of GaAs for the middle cell.In order to obtain maximum conversion efficiency for triple-junction solar cells,it is essential to narrow down the middle cell band gap to 1.2eV and increase the short-circuit current density by 2mA/cm 2compared with that of the GaAs middle cell.When the material is replaced with a narrower band gap,the output voltage will drop.However,the effect of improving the electric current balance out-performs this drop in output voltage and boosts the effi-ciency of the entire multi-junction cell.When a crystal with such a narrow band gap is grown on a Ge base material,lattice relaxation will occur in the middle of epitaxial crystal growth because the lattice constants of narrower band-gap materials are larger than that of Ge (as shown in Fig.2).As a result,the carrier transport properties will degrade due to dislocation.Researchers from the international research center Solar Quest,the University of Tokyo,aim to move beyond such material-related restrictions,and obtain materials and structures that have effective narrow band gaps while maintaining lattice matching with Ge or GaAs.To achieve this goal,we have taken three approaches as indicated in Fig.3.These approaches are explained in detail below.DILUTE NITROGEN-ADDED BULK CRYSTAL Indium gallium nitride arsenide (InGaNAs)is a bulk material consists of InGaAs,which contains several percent of nitrogen.InGaNAs has a high potential for achieving a narrow band gap while maintaining lattice matching with Ge or GaAs.However,InGaNAs has a fatal problem,that is,a drop in carrier mobility due to inhomogeneousdistribution of nitrogen (N).To achieve homogeneous solid solution of N in crystal,we have applied atomic hydrogen irradiation in the film formation process and addition of a very small amount of antimony (Sb)(Fig.3).The atomic hydrogen irradiation technology and the nitrogen radical irradiation technology for incorporating N efficiently into the crystal can be achieved only through molecular beam epitaxy (MBE),which is used to fabricate films under high vacuum conditions.(Nitrogen radical irradiation is a technology that irradiates the surface of a growing crystal with nitrogen atoms that are resolved by passing nitrogen through a plasma device attached to the MBE system.)Therefore,high-quality InGaNAs has been obtained only by MBE until now.Furthermore,as a small amount of Sb is also incorporated in a crystal,it is nec-essary to control the composition of five elements in the crystal with a high degree of accuracy to achieve lattice matching with Ge or GaAs.We have overcome this difficulty by optimizing the crystal growth conditions with high precision and devel-oped a cell that has an InGaNAs absorption layer formed on a GaAs substrate.The short-circuit current has increased by 9.6mA/cm 2for this cell,compared with a GaAs single-junction cell,by narrowing the band gap down to 1.0eV.This technology can be implemented not only for triple-junction cells,but also for higher efficiency lattice-matched quadruple-junction cells on a Ge substrate.In order to avoid the difficulty of adjusting the compo-sition of five elements in a crystal,we are also taking an approach of using GaNAs with a lattice smaller than that of Ge or GaAs for the absorption layer and inserting InAs with a large lattice in dot form to compensate for the crystal’s tensile strain.To make a solid solution of N uniformly in GaNAs,we use the MBE method for crystal growth and the atomic hydrogen irradiation as in the case of InGaNAs.We also believe that using 3D-shaped InAs dots can effectively compensate for the tensile strainthatFig.1Solar spectrum radiated on earth and photon flux collected by the top cell (InGaP),middle cell (GaAs),and bottom cell (Ge)(equivalent to the area of the filled portions in the figure)occurs in GaNAs.We have measured the characteristics of a single-junction cell formed on a GaAs substrate by using a GaNAs absorption layer with InAs dots inserted.Figure 4shows that we were able to succeed in enhancing the external quantum efficiency in the long-wavelength region (corresponding to the GaNAs absorp-tion)to a level equal to GaAs.This was done by extending the absorption edge to a longer wavelength of 1200nm,and increasing the thickness of the GaNAs layer by increasing the number of laminated InAs quantum dot layers.This high quantum efficiency clearly indicates that GaNAs with InAs dots inserted has the satisfactory quality for middle cell material (Oshima et al.2010).STRAIN-COMPENSATED QUANTUM WELL STRUCTUREIt is extremely difficult to develop a narrow band-gap material that can maintain lattice matching with Ge orGaAs unless dilute nitrogen-based materials mentioned earlier are used.As shown in Fig.2,the conventionally used material InGaAs has a narrower band gap and a larger lattice constant than GaAs.Therefore,it is difficult to grow InGaAs with a thickness larger than the critical film thickness on GaAs without causing lattice relaxation.However,the total film thickness of InGaAs can be increased as an InGaAs/GaAsP strain-compensated multi-layer structure by laminating InGaAs with a thickness less than the critical film thickness in combination with GaAsP that is based on GaAs as well,but has a small lattice constant,and bringing the average strain close to zero (Fig.3.).This InGaAs/GaAsP strain-compensated multilayer structure will form a quantum well-type potential as shown in Fig.5.The narrow band-gap InGaAs layer absorbs the long-wavelength photons to generate electron–hole pairs.When these electron–hole pairs go over the potential bar-rier of the GaAsP layer due to thermal excitation,the electrons and holes are separated by a built-in electricfieldFig.2Relationship between band gaps and lattice constants of III–V-based and IV-based crystalsto generate photocurrent.There is a high probability of recombination of electron–hole pairs that remain in the well.To avoid this recombination,it is necessary to take out the electron–hole pairs efficiently from the well and transfer them to n-type and p-type regions without allowing them to be recaptured into the well.Designing thequantumFig.3Materials and structures of narrow band-gap middle cells being researched by thisteamFig.4Spectral quantum efficiency of GaAs single-junction cell using GaNAs bulk crystal layer (inserted with InAs dots)as the absorption layer:Since the InAs dot layer and the GaNAs bulk layer are stacked alternately,the total thickness of GaNAs layers increases as the number of stacked InAs dot layers is increased.The solid line in the graph indicates the data of a reference cell that uses GaAs for its absorption layer (Oshima et al.2010)well structure suited for this purpose is essential for improving conversion efficiency.The high-quality crystal growth by means of the metal-organic vapor phase epitaxy (MOVPE)method with excellent ability for mass production has already been applied for InGaAs and GaAsP layers in semiconductor optical device applications.Therefore,it is technologically quite possible to incorporate the InGaAs/GaAsP quantum well structure into multi-junction solar cells that are man-ufactured at present,only if highly accurate strain com-pensation can be achieved.As the most basic approach related to quantum well structure design,we are working on fabrication of super-lattice cells with the aim of achieving higher efficiency by making the GaAsP barrier layer as thin as possible,and enabling carriers to move among wells by means of the tunnel effect.Figure 6shows the spectral quantum effi-ciency of a superlattice cell.In this example,the thickness of the GaAsP barrier layer is 5nm,which is not thin enough for proper demonstration of the tunnel effect.When the quantum efficiency in the wavelength range (860–960nm)that corresponds to absorption of the quan-tum well is compared between a cell,which has a con-ventionally used barrier layer and a thickness of 10nm or more,and a superlattice cell,which has the same total layer thickness of InGaAs,the superlattice cell demonstrates double or higher quantum efficiency.This result indicates that carrier mobility across quantum wells is promoted by even the partial use of the tunnel effect.By increasing the P composition in the GaAsP layer,the thickness of well (or the In composition)can be increased,and the barrier layer thickness can be reduced while strain compensation is maintained.A cell with higher quantum efficiency can befabricated while extending the absorption edge to the long-wavelength side (Wang et al.2010,2012).GROWTH TECHNIQUE FOR STRAIN-COMPENSATED QUANTUM WELLTo reduce the strain accumulated in the InGaAs/GaAsP multilayer structure as close to zero as possible,it is nec-essary to control the thickness and atomic content of each layer with high accuracy.The In composition and thickness of the InGaAs layer has a direct effect on the absorption edge wavelength and the GaAsP layer must be thinned to a satisfactory extent to demonstrate fully the tunnel effect of the barrier layer.Therefore,it is desirable that the average strain of the entire structure is adjusted mainly by the P composition of the GaAsP layer.Meanwhile,for MOVPE,there exists a nonlinear rela-tionship between the P composition of the crystal layer and the P ratio [P/(P ?As)]in the vapor phase precursors,which arises from different absorption and desorption phenomena on the surface.As a result,it is not easy to control the P composition of the crystal layer.To break through such a difficulty and promote efficient optimiza-tion of crystal growth conditions,we have applied a mechanism to evaluate the strain of the crystal layer during growth in real time by sequentially measuring the curvature of wafers during growth with an incident laser beam from the observation window of the reactor.As shown in Fig.7,the wafer curvature during the growth of an InGaAs/GaAsP multilayer structure indicates a periodic behavior.Based on a simple mechanical model,it has become clear that the time changes ofwaferFig.5Distribution of potential formed by the InGaAs/GaAsP strain-compensated multilayer structure:the narrow band-gap InGaAs layer is sandwiched between wide band-gap GaAsP layers and,as a result,it as quantum well-type potential distribution.In the well,electron–hole pairs are formed by absorption of long-wavelength photons and at the same time,recombination of electrons and holes takes place.The team from Solar Quest is focusing on developing a superlattice structure with the thinnest GaAsP barrier layercurvature are proportionate to the strain of the crystal layer relative to a substrate during the growing process.One vibration cycle of the curvature is same as the growth time of an InGaAs and GaAsP pair (Sugiyama et al.2011).Therefore,the observed vibration of the wafer curvature reflects the accumulation of the compression strain that occurs during InGaAs growth and the release of the strain that occurs during GaAsP growth.When the strain is completely compensated,the growth of the InGaAs/GaAsP pair will cause this strain to return to the initial value and the wafer curvature will vibrate with the horizontal line as the center.As shown in Fig.7,strain can be compensated almost completely by adjusting the layer structure.Only by conducting a limited number of test runs,the use of such real-time observation technology of the growth layer enables setting the growth conditions for fabricating the layer structure for which strain has been compensated with highaccuracy.Fig.6Spectral quantum efficiency of GaAs single-junction cell using InGaAs/GaAsP superlattice as theabsorption layer:This structure consists of 60layers of InGaAs quantum wells.The graph also shows data of a reference cell that uses GaAs for its absorption layer (Wang et al.2010,2012)Fig.7Changes in wafer curvature over time during growth of the InGaAs/GaAsP multilayer structure.This graph indicates the measurement result and the simulation result of the curvature based on the layer structure(composition ?thickness)obtained by X-ray diffraction.Since compressive strain is applied during InGaAs growth,the curvature decreases as time passes.On the other hand,since tensile strain is applied during GaAsP growth,the curvature changes in the oppositedirection (Sugiyama et al.2011)FUTURE DIRECTIONSIn order to improve the conversion efficiency by enhancing the current matching of multi-junction solar cells using III–V compound semiconductors,there is an urgent need to create semiconductor materials or structures that can maintain lattice matching with Ge or GaAs,and have a band gap of1.2eV.As for InGaNAs,which consists of InGaAs with several percent of nitrogen added,we have the prospect of extending the band edge to1.0eV while retaining sufficient carrier mobility for solar cells by means of atomic hydrogen irradiation and application of a small quantity of Sb during the growth process.In addition,as for GaNAs bulk crystal containing InAs dots,we were able to extend the band edge to1.2eV and produce a high-quality crystal with enoughfilm thickness to achieve the quantum efficiency equivalent to that of GaAs.These crystals are grown by means of MBE. Therefore,measures that can be used to apply these crys-tals for mass production,such as migration to MOVPE, will be investigated after demonstrating their high effi-ciency by embedding these crystals into multi-junction cells.As for the InGaAs/GaAsP strain-compensated quantum well that can be grown using MOVPE,we are working on the development of a thinner barrier layer while compen-sating for the strain with high accuracy by real-time observation of the wafer curvature.We have had the prospect of achieving a quantum efficiency that will sur-pass existing quantum well solar cells by promoting the carrier transfer within the multilayer quantum well struc-ture using the tunnel effect.As this technology can be transferred quite easily to the existing multi-junction solar cell fabrication process,we strongly believe that this technology can significantly contribute to the efficiency improvement of the latest multi-junction solar cells. REFERENCESOshima,R.,A.Takata,Y.Shoji,K.Akahane,and Y.Okada.2010.InAs/GaNAs strain-compensated quantum dots stacked up to50 layers for use in high-efficiency solar cell.Physica E42: 2757–2760.Sugiyama,M.,K.Sugita,Y.Wang,and Y.Nakano.2011.In situ curvature monitoring for metalorganic vapor phase epitaxy of strain-balanced stacks of InGaAs/GaAsP multiple quantum wells.Journal of Crystal Growth315:1–4.Wang,Y.,Y.Wen,K.Watanabe,M.Sugiyama,and Y.Nakano.2010.InGaAs/GaAsP strain-compensated superlattice solar cell for enhanced spectral response.In Proceedings35th IEEE photovoltaic specialists conference,3383–3385.Wang,Y.P.,S.Ma,M.Sugiyama,and Y.Nakano.2012.Management of highly-strained heterointerface in InGaAs/GaAsP strain-balanced superlattice for photovoltaic application.Journal of Crystal Growth.doi:10.1016/j.jcrysgro.2011.12.049. AUTHOR BIOGRAPHYYoshiaki Nakano(&)is Professor and Director General of Research Center for Advanced Science and Technology,the University of Tokyo.His research interests include physics and fabrication tech-nologies of semiconductor distributed feedback lasers,semiconductor optical modulators/switches,monolithically integrated photonic cir-cuits,and high-efficiency heterostructure solar cells.Address:Research Center for Advanced Science and Technology, The University of Tokyo,4-6-1Komaba,Meguro-ku,Tokyo153-8904,Japan.e-mail:nakano@rcast.u-tokyo.ac.jp。