a r X i v :0707.0586v 2 [c o n d -m a t .m e s -h a l l ] 18 J u l 2007
Numerical studies of the Pfa?an model of the ν=
5
2
.We examine it for the quasihole excitations by comparison with exact diagonalization results.Speci?cally,we consider the structure of the low-energy spectrum,accuracy of the microscopic wave functions,particle-hole symmetry,splitting of the degeneracies,and o?-diagonal long range order.We also review how the 5/2FQHE can be understood without appealing to the Pfa?an model.Implications for nonabelian braiding statistics will be mentioned.
I.INTRODUCTION
5/2is the only even denominator fraction securely ob-served in a single layer fractional quantum Hall e?ect (FQHE)1,2,3.(The fraction 7/2is trivially related to it by particle hole symmetry in the second Landau level.)The model of noninteracting composite fermions predicts a compressible Fermi sea at half ?lled lowest Landau level,which provides a good description of the compressible state here 4,5.A promising scenario for the incompress-ible state at the half ?lled second Landau level at ν=5/2is based on the idea of pairing of composite fermions,de-scribed by a Pfa?an wave function 6,7.Several studies have supported this interpretation 8,9,10,11,12.
The Pfa?an wave function is the exact ground state of a singular three-body model interaction (cf.Eq.2be-low).Exact solutions for quasiholes are also available for this model interaction.A case has been made,both from analytical arguments 6,13,14and numerical calculations 15,that these Pfa?an quasiholes have the remarkable prop-erty of nonabelian braiding statistics.Recently,the non-abelian statistics has taken additional importance be-cause of proposals to test it experimentally 16,17,18,and to exploit it for quantum computation 16,19,20,21.That makes it important to perform an examination of the applicability of the Pfa?an model to the real,Coulomb solution.The Coulomb ground state wave function has been compared to the Pfa?an ground state wave function in the past 8,12and found to have overlaps in the range 0.69-0.87for 8to 16particles.Our recent comparisons of the Pfa?an quasiholes and the real Coulomb quasiholes 22showed a worse agreement.Because the route to non-Abelions is via the Pfa?an model and the degeneracies it implies,these studies have relevance to nonabelian braid-ing statistics as well.
This paper brie?y reviews our previous work,at the same time providing many new results relevant to this problem.In Sec.II the Pfa?an model is de?ned and some relevant results are reviewed.In Sec.III we com-ment on the particle-hole symmetry violation by the Pfaf-?an family of states.In Sec.IV the absence of o?-diagonal long range order in the Pfa?an state is pointed out,and the relevance of this ?nding is discussed.In Sec.VI we check the assertion,commonly made in the literature,that the energy di?erence of the quasihole
states,that are degenerate for the three-body model in-teraction,remains exponentially small for the Coulomb interaction.In Sec.VII we attempt to separate the pos-tulated charge 1
2
FQHE.Short reports on parts of this paper have appeared elsewhere 22,23.
II.THE PF AFFIAN MODEL
Throughout this article we will assume that the low-est Landau level (LL)is full and inert,and the two-dimensional electron gas in the second LL is fully po-larized.All calculations are performed in the spherical geometry.The objective is to determine the ground state and the low-energy excitations for the Coulomb interac-tion
V (C)=
e 2
|r i ?r j |
,
(1)
in second LL at ?lling factor ν=1/2(?is the static di-electric constant of the host semiconductor).This prob-lem is equivalent to electrons in the lowest Landau level interacting with an e?ective interaction V e?.We will use the lowest LL to simulate the second LL physics in what follows.
The “Pfa?an model”considers a three-body model interaction 7,14,which in the spherical geometry takes the form
V
Pf
=
e 2
2
ν=1/2(Moore and Read 6):
ΨPf
0=Pf
1(z i ?z j )
Φ21.
(4)
For two coincident quasiholes,η1=η2≡η,this reduces
to a charge 1
4
associated with it.Unlike for the vortex,the density does not vanish at the center of a quasihole.Analogous wave functions can be written for an even number (2m )of quasiholes.Exact wave functions for quasiparticles are not available.
Several wave functions can be associated for a given con?guration of 2m quasiholes,
which correspond,in the appropriate generalization of Eq.(4)to 2m quasiholes,to di?erent ways of grouping half of the ηk ’s with z i and the other half with z j .It has been shown 13that only 2m ?1of these functions are linearly independent.Adiabatic braiding of quasiholes (which is feasible for a gapped sys-tem)can take the system from one linear combinations of PfQH states to another,which lies at the origin of nonabelian statistics of quasiholes.
To study bulk properties,it is convenient to formu-late the problem of interacting electrons in the spheri-cal geometry,in which the electrons move on the surface of a sphere and a radial magnetic ?eld is produced by a magnetic monopole of strength Q at the center.24,25Here 2Qφ0is the magnetic ?ux through the surface of the sphere;φ0=hc/e ,and 2Q is an integer by Dirac’s quan-tization condition.Then wave functions in Eqs.(3-5),which are written for the disk geometry,can be mapped to the sphere by the stereographic mapping 25,which amounts to the substitution
(z a ?z b )→(u a v b ?v a u b ),
(6)
for all coordinate di?erences,where u a =cos θa
2e
iφa /2
are spinorial coordinates on the sphere.The orbital angular momentum quantum number is denoted by L .
III.
PARTICLE-HOLE SYMMETRY
The exact Coulomb eigenstates in any given Landau level satisfy particle-hole symmetry,i.e.,the exact eigen-states at νand 1?νare related by particle-hole transfor-mation.The wave functions in the CF theory 26satisfy particle hole symmetry to a very good approximation,even though there is no symmetry principle that so re-quires.For example,the wave functions at ν=n/(2n ?
1),given by Ψn/(2n ?1)=P LLL Φ21[Φn ]?
,are almost identi-cal to the those obtained by particle-hole transformation of the wave functions Ψn ′/(2n ′+1)=P LLL Φ21Φn ′,with
n =n ′
+1.
The three body interaction does not satisfy particle-hole (p-h)symmetry.To get a feel for the extent to which this symmetry is broken,we have considered the system of N =8particles at 2Q =15.In this case,particle hole transformation gives eight holes (to be dis-tinguished from quasi holes)at 2Q =15.We obtain the exact spectrum of the V Pf model interaction,which is given in the upper left panel of Fig.1.This system cor-responds to four quasiholes,and has a number of zero energy states,which form the Pfa?an quasihole sector.We obtain the particle-hole conjugate of each eigenstate,called Ψc ,and calculate its energy expectation value for the V Pf interaction.When there are several degenerate Pfa?an quasihole states,we diagonalize V Pf in the sub-space of the p-h conjugate states to obtain the energies.The resulting spectrum is shown in the top right column of Fig. 1.(For the Coulomb interaction,this exercise would produce a spectrum identical to the original one,apart from an overall energy shift.)We construct sym-metrized states Ψs ∝(Ψ+Ψc ),which satisfy particle-hole symmetry by construction;the resulting spectrum for these states is given in the lower left panel of Fig.1.The lower right spectrum is for antisymmetrized states Ψa ∝(Ψ?Ψc ).
Table 1shows the squared overlaps between the orig-inal Pfa?an quasihole states with the various states ob-tained with the help of p-h conjugation.To handle the multiplicity of the PfQH sector for L =0,2,4,6(cf.Fig.1),the overlap between two subspaces has been de-?ned in a basis-independent manner (see caption of Table 1).The overlaps are not particularly high;for example,in the L =0part of the quasihole branch,which contains two states for N =8,the overlap is 0.511,and deterio-rates for higher L ’s.Similar numbers are obtained for other states in the PfQH sector.The near orthogonality of Ψand Ψc at L =8is accompanied by a very high energy of Ψc .
These results demonstrate a substantial breakdown of the p-h symmetry by the V Pf interaction.The Pfaf-?an quasihole band is absent in all of the new spectra;the states derived from the Pfa?an quasihole band are mixed up with other states.It has been shown 11that the particle-hole symmetrization (Ψ→Ψs )of the Pfa?an wave function improves the overlap with the Coulomb ground state.Our results show,however,that this also
3
destroys the degeneracy of PfQH sector.One can ask whether the nonabelian statistics of the Pfa?an quasi-holes is robust to p-h symmetrization;we are not able resolve this question de?nitively by a direct calculation of the braiding phases,which requires much larger sys-
FIG.1:Upper left panel shows the original spectrum of V Pf with N=8,2Q=2N?1(four quasiholes);the Pfa?an quasihole states have zero energy.Also shown are the spectra for the p-h conjugate states(top right),the p-h symmetrized
states(bottom left),and p-h antisymmetrized states(bottom right).The diamonds show the states derived from the Pfaf-?an quasihole branch.
symmetric
conjugate combination
0.5110.575
O(L=2)0.542
0.3570.201
O(L=4)0.641
0.0010.489
O(L=6)0.443
4×10?70.500
TABLE I:Squared overlaps between the subspaces spanned by the zero-energy states and the subspaces spanned by their particle-hole conjugate,particle-hole symmetrized,and particle-hole antisymmetrized images,respectively.Squared overlaps are de?ned as O=P N i,j| Ψ4?qh,i|Ψ′4?qh,j |2/N, where N is the number of degenerate multiplets14of V Pf at
L,and i,j=1,···,N.
IV.OFF-DIAGONAL LONG RANGE ORDER
We wish to stress that the Pfa?an wave function does not represent a true superconductor;the pairing of com-posite fermions opens a gap to produce FQHE but does not establish long range phase coherence in the electronic
state.For this purpose,we calculate the o?-diagonal long range order parameter:
|G(r1,r2,r′1,r′2)|= Ψ0|?ψ?(r′1)?ψ?(r′2)?ψ(r2)?ψ(r2)|Ψ0 ,
(7) where?ψ(r)and?ψ?(r)are the usual annihilation and cre-ation?eld operators.We place the primed coordinates
near the north pole,separated by a distance equal to the magnetic length,and the unprimed coordinates at the south pole,also separated by a distance equal to the
magnetic length.The results in Table II,obtained by Monte Carlo calculation,demonstrate the absence of o?-
diagonal long-range order in the Pfa?an wave function.
N
4
0.001(2)
8
0.0002(5)
TABLE II:O?-diagonal long-range order parameter G(r1,r2,r′1,r′2)with r1and r2separated by l B about
the north pole,and r′1and r′2separated by l B about the
south pole for the paired CF wave function Pf(1/(z i?z j))Φ21.
V.TESTING THE PF AFFIAN QUASIHOLE
W A VE FUNCTION
We have recently carried out comparisons between the Pfa?an and Coulomb quasiholes22.Figs.2,3,
and4show the spectra for states with two and four quasiholes for N=10and12electrons.For10elec-
trons,the Pfa?an model predicts zero energy states at L=1,3,5and L=02,10,24,31,44,52,63,71,82,90,101,
respectively(the superscript denotes the degeneracy),for two and four quasiholes.These states form the Pfa?an
quasihole band.For12electrons,the Pfa?an quasihole band contains states at L=0,2,4,6for two quasiholes
and L=03,10,24,32,45,52,65,72,83,91,102,110,121for four quasiholes.For14electrons,the Pfa?an quasihole band for two quasiholes has states at angular momenta
L=1,3,5,7.
The Coulomb spectra in Figs.2-4do not show
well de?ned bands that have a one-to-one correspon-dence with the Pfa?an quasihole bands.Ref.22gives
overlaps between the Pfa?an and Coulomb quasihole states,which are generally worse than for the ground
state.Fig.5depicts for the two quasihole state (for14electrons)the“total overlap,”de?ned as O= L=1,3,5,7| ΨL2?qh|ΨL coul |2/4where|ΨL2?qh is the two quasihole state with L z=L and|ΨL coul is the Coulomb
ground state with L z=L.This?gure shows the depen-dence of the overlap on the form of the interaction;by
FIG.2:Spectra atν=5
2for the model interaction V Pf(left
column),and the second Landau level Coulomb interaction (right column)for N=12particles for two(upper row)and four(lower row)quasiholes.
increasing the V1pseudopotential of the Coulomb inter-action by0.03units,it is possible to increase the overlap from0.3to0.6.For largeδV1,the solution is essen-tially the lowest-LL Coulomb solution;Fig.5thus shows that the Pfa?an wave functions provide a comparable description of the state in the lowest two Landau levels.
ε
2
B 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2 4 6 8 10 12 14
L
e
n
e
r
g
y
[
a
r
b
.
u
n
i
t
s
]
0 2 4 6 8 10 12 14
L
?4.47
?4.46
?4.45
?4.44
?4.43
?4.42
?4.41
?4.4
?4.48
e
n
e
r
g
y
[
e
/
l
] FIG.4:Spectra atν=5
culation is currently not feasible.
The calculation requires at least four quasiholes,which we place on the sphere at maximal separation,i.e.at the vertices of a regular tetrahedron.The Coulomb interac-tion in the?rst and second LLs is diagonalized in the space spanned by two Pfa?an quasihole wave functions. The overlap and interaction matrices are calculated by Monte Carlo methods;an orthonormal basis is found by the standard Gram-Schmidt procedure;and the interac-tion is diagonalized in this basis.The Coulomb interac-tion in the second LL is simulated in the lowest LL by an e?ective interaction of the form
1
V e?(r)=
6
ence of delta function impurities that attract the quasi-holes.We take the impurities to be placed at one or both of the poles so the eigenfunctions have a well de?ned L z (although they do not have a well de?ned L quantum number).We also assume su?ciently weak strengths for the impurity potential,so they do not cause a mixing of the Pfa?an quasihole states with higher energy states.Our principal results are as follows.
(b) ψ(3)
2?qh ψ
2?qh
(d) c, 2 deltas ψ
2?qh
(c) c,1 delta ψ2?qh
(a) pf
ψ2?qh
(a) pf
(b) ψ(3)
2?qh
ψ2?qh
(c) c,1 delta
ψ2?qh
(d) c, 2 deltas
θθN=12N=14N=16
0.6 0.8 1 1.2 1.4 0
0.1 0.2 0.3 0.4
0.5 0
0.1 0.2 0.3 0.4
0.5 0 0.5 1 1.5 2 2.5 3
Q /e
?Q /e
?Q /e
?Q /e
? 0
0.1 0.2 0.3 0.4
0.5 0.2
0.4 0.6 0.8 1 1.2 1.4ρ
ρ
ρ
(rad) 0.8
0.9 1 1.1 1.2 1.3 0
0.5
1
1.5
2
2.5
3
0.9
1 1.1 1.
2 1.3(rad)
0 0.2 0.3 0.4
0.5 0.1ρ
FIG.9:Left panel:Charge densities of two quasihole states for (a)the Pfa?an wave function with two quasiholes at two poles;(b)the ground state of V Pf with two delta function im-purities;(c)the Coulomb ground state with one delta func-tion impurity;(d)the Coulomb ground state with two im-purities.The impurities are placed on the two poles (or one pole in case of a single impurity),so the eigenstates have a well de?ned L z .The results are for N =12(dashed lines),N =14(dotted lines)and N =16(solid lines)electrons at 2Q =2N ?2.The density in (a)is calculated by Monte Carlo,and in other panels from exact diagonalizaion.When the ground state has L z =0,there are two degenerate states at ±L z ;we have shown only one of them for simplicity.The normalization is chosen to ensure that the integrated density equals N .Right panel:the integrated excess charge for each density,normalized so that the total charge excess is 1
4
,as approximately seen in the top panel.This ?gure is taken from Ref.22.
For the V Pf model a single delta function impurity in the lowest LL localizes a vortex (which is a combination of two quasiholes)rather than a single Pfa?an quasihole for the following reason.The energy of a given wave function is equal to a properly weighted average of the
densities at the positions of the delta functions (for weak impurity strengths).For a delta function at (U,V ),the lowest energy state (which has zero energy independent of the strength of the delta impurity)is the one in which both quasiholes localize at (U,V ),producing a vortex ΨV with vanishing density at (U,V ).Surprisingly,as seen in Fig.9(b),even two delta impurities fail to separate two quasiholes,even though the systems are su?ciently large at least for the charge-1/4Pfa?an quasiholes to be well separated (top panels)
For two Coulomb quasiholes,at ?rst sight,one may expect that even a single delta function should produce well separated quasiholes,because it can bind one of them,which then should repel the other.As seen in Fig.9(c,d),neither one nor two delta functions produce separated quasiholes.In fact,the charge pro?le is prac-tically identical for the two cases.The situation is more restrictive for the Coulomb interaction because,instead of many degenerate states,we have a single ground state multiplet with a de?nite L .All that weak disorder can do is cause a mixing between the di?erent L z components of the ground state multiplet.For the case of two delta functions at the two poles,L z is a good quantum num-ber,so the delta functions only lift the degeneracy of the L z states.The lack of quasihole separation in space is attributable to the fact that the ground state now has a more or less de?nite L .The absence of exact degeneracy inhibits quasihole localization.
VIII.
IMPLICATIONS FOR BRAIDING
STATISTICS
The Pfa?an quasiholes are believed to obey non-abelian braiding statistics.Our ?nite system studies of the Coulomb solutions do not provide a clear con?rma-tion of the Pfa?an model,and therefore of the non-abelian statistics.We cannot rule out the possibility that the Pfa?an physics will be recovered in the ther-modynamic limit.It is useful to recall,in this context,how the fractional abelian braiding statistics 27,28,29of the quasiparticles of the ν=n/(2n +1)states has been con-?rmed theoretically.There,the CF theory provides a qualitatively valid description the quasiparticle band,as well as accurate wave functions.These wave functions are then used for large systems to establish the abelian statistics 30,31.These calculations also demonstrate that the braiding statistics is not well de?ned when quasi-particles are overlapping,which is why its con?rmation requires large systems.The nonavailability of accurate wave functions for the 5/2quasiparticles or quasiholes prevents similar calculations of their braiding properties.
IX.AN ALTERNATIVE APPROACH FOR5/2
FQHE
It is not known how the Pfa?an wave functions can be improved for the two body Coulomb interaction,due to lack of variational parameters.Further,the pairing of composite fermions is viewed as arising from an in-stability of the CF Fermi sea7,10,32,but the CF Fermi sea is not a limiting case of the Pfa?an wave function.
These observations have motivated us to approach the 5/2FQHE from the CF Fermi sea end,without assuming any pairing at the outset23.The idea is straightforward. We know that noninteracting composite fermions do not show FQHE at5/2;our approach is to include the resid-ual interactions between them by constructing a basis of“noninteracting,”or the“unperturbed,”CF ground and excited states and rediagonalizing the Coulomb in-teraction in that subspace to obtain the spectrum for “interacting”composite fermions.This is known as the CF diagonalization,and the relevant techniques are de-scribed in the literature33,34.As usual,we simulate the second LL physics in the lowest LL by working with an appropriate e?ective interaction.We work at the same ?ux value as the Pfa?an wave function,but because of a technical reason23,we work with holes,rather than elec-trons.(Holes are not to be confused with quasiholes.)By particle hole symmetry,the number of holes is given by N h=(2Q+1)?N=N?2at2Q=2N?3.In what fol-lows,composite fermions are made by attaching vortices to holes rather than electrons.We show results at“ze-roth order”CF diagonalization(when only the lowest en-ergy unperturbed states are considered)and“?rst order”CF diagonalization(which also includes states with one higher unit of“kinetic energy”).The composite fermion kinetic energy levels are calledΛlevels.
Figure10shows the excitation spectra at the half?lled second LL for N h=12,14,16and20obtained by CF diagonalization at the zeroth and the?rst orders. (N h=18is not considered as it aliases withν=3
2
FQHE.Although there is some ambiguity as to which excitation is to be identi?ed with the transport gap(corresponding to a far separated quasiparticle-quasihole pair),an inspection indicates a gap of～0.02,which is consistent with the earlier results from exact diagonalization8,35.
Figure11shows analogous results for the half?lled lowest LL.The zeroth order CF diagonalization gener-ates the lowest band,and the?rst order generates the next band.The energies of states in the lowest band do not change appreciably from zeroth to the?rst order. The energy gap between the two lowest bands can be understood as the energy cost of exciting one more CF particle-hole pair.No such bands are seen for half?lled second LL.
It is not known how this description of the5/2FQHE relates to the Pfa?an model.In particular,a natural description of the quasiparticles is as excited composite fermions(which are heavily renormalized by the residual interaction).From this perspective,there is no reason to suspect that they would obey nonabelian statistics, although that cannot be ruled out as the residual inter-action causes nonperturbative change.
X.ACKNOWLEDGMENT
We thank IDRIS-CNRS for a computer time alloca-tion,the High Performance Computing(HPC)group at Penn State University ASET(Academic Services and Emerging Technologies)for assistance and computing time on the Lion-XL and Lion-XO clusters.Partial sup-port of this research by the National Science Foundation is gratefully acknowledged.
1R.Willett,J.P.Eisenstein,H.L.Stormer,D.C.Tsui, A.C.Gossard,and J.H.English,Phys.Rev.Lett.59, 1776(1987).
2W.Pan,J.-S.Xia,V.Shvarts,D.E.Adams,H.L.Stormer, D.C.Tsui,L.N.Pfei?er,K.W.Baldwin,and K.W.West, Phys.Rev.Lett.83,3530(1999).
3J.P.Eisenstein,K. B.Cooper,L.N.Pfei?er,and K.W.West,Phys.Rev.Lett.88,076801(2002).
4V.Kalmeyer and S.C.Zhang,Phys.Rev.B46,R9889 (1992);B.I.Halperin,P.A.Lee,and N.Read,Phys.Rev. B47,7312(1993).
5R.L.Willett,R.R.Ruel,K.W.West,and L.N.Pfei?er,
Phys.Rev.Lett.71,3846(1993);W.Kang,H.L.Stormer, L.N.Pfei?er,K.W.Baldwin,and K.W.West,Phys.
Rev.Lett.71,3850(1993);V.J.Goldman,B.Su,and J.K.Jain,Phys.Rev.Lett.72,2065(1994);J.H.Smet et al.,Phys.Rev.Lett.77,2272(1996).
6G.Moore and N.Read,Nucl.Phys.B360,362(1991). 7M.Greiter,X.G.Wen,and F.Wilczek,Phys.Rev.Lett.
66,3205(1991);Nucl.Phys.B374,567(1992).
8R.H.Morf,Phys.Rev.Lett.80,1505(1998).
9K.Park,V.Melik-Alaverdian,N.E.Bonestel,and J.K.
Jain,Phys.Rev.B58,R10167(1998).
10V.W.Scarola,K.Park,and J.K.Jain,Nature406,863
FIG.10:Zeroth-order(top)and?rst-order(bottom)CF diagonalization excitation spectra for N h=12,14,16,20holes in the second Landau level.
(2000).
11E.H.Rezayi and F.D.M.Haldane,Phys.Rev.Lett.84, 4685(2000).
12V.W.Scarola,J.K.Jain,E.H.Rezayi,Phys.Rev.Lett.88, 216804(2002).
13C.Nayak and F.Wilczek,Nucl.Phys.B479,529(1996). 14N.Read and E.H.Rezayi,Phys.Rev.B54,16864(1996). 15Y.Tserkovnyak and S.H.Simon,Phys.Rev.Lett.90, 016802(2003).
16S.Das Sarma,M.Freedman,and C.Nayak,Phys.Rev.
Lett.94,166802(2005).
17A.Stern and B.I.Halperin,Phys.Rev.Lett.96,016802 (2006).
18P.Bonderson,A.Kitaev,and K.Shtengel,Phys.Rev.Lett.
96,016803(2006).
19M.Freedman,C.Nayak,and K.Walker,Phys.Rev.B73, 245307(2006).
20P.Bonderson,K.Sthengel,and J.K.Slingerland,Phys.
Rev.Lett.97,016401(2006).
21C.Bena and C.Nayak,Phys.Rev.B73,133335(2006). 22C.T?o ke,N.Regnault,and J.K.Jain,Phys.Rev.Lett.98, 036806(2006).
23C.T?o ke and J.K.Jain,Phys.Rev.Lett.96,246805(2006). 24F.D.M.Haldane,Phys.Rev.Lett.51,605(1983);also in The Quantum Hall E?ect,edited by R.E.Prange and
S.M.Girvin(Springer,New York,1987).
25G.Fano,F.Ortolani,and E.Colombo,Phys.Rev.B34, 2670(1986).
26J.K.Jain,Phys.Rev.Lett.63,199(1989);Physics Today 53(4),39(2000).
27J.M.Leinaas and J.Myrheim,Nuovo Cimento B37,1 (1977).
28B.I.Halperin,Phys.Rev.Lett.52,1583(1984).
29D.P.Arovas,J.R.Schrie?er,and F.Wilczek,Phys.Rev.
Lett.53,722(1984).
30H.Kj?nsberg and J.Myrheim,Int.J.Mod.Phys.A14, 537(1999);H.Kj?nsberg and J.M.Leinaas,Nucl.Phys.B 559,705(1999).
31G.S.Jeon,K.L.Graham,J.K.Jain,Phys.Rev.Lett.91, 036801(2003);Phys.Rev.B70,125316(2004).
32M.Greiter,X.G.Wen,and F.Wilczek,Phys.Rev.B46, 9586(1992).
33J.K.Jain and R.K.Kamilla,Int.J.Mod.Phys.B11, 2621(1997);Phys.Rev.B55,R4895(1997).
34S.S.Mandal and J.K.Jain,Phys.Rev.B66,155302 (2002).
35R.H.Morf,N.d’Ambrumenil,and S.Das Sarma,Phys.
Rev.B66,075408(2002).
9
九年级课文翻译 Document serial number【NL89WT-NY98YT-NC8CB-NNUUT-NUT108】
人教版初中英语九年级U n i t3课文翻译 SectionA2d 何伟：这是欢乐时光公园——我所在城市最大的游乐园！ 艾丽斯：要尝试一些乘骑项目，我好兴奋呀！ 何伟：我们应该从哪里开始玩呢？有太空世界、水上世界、动物世界…… 艾丽斯：哦，你能先告诉我哪儿有洗手间吗？ 何伟：什么休息室你想要休息吗但是我们还没有开始玩呢！ 艾丽斯：哦，不是，我的意思不是休息间。我的意思是……你知道的，卫生间或盥洗室。何伟：嗯……那么你是指……厕所？ 艾丽斯：正是！对不起，也许“洗手间”一词在中国不常用。 何伟：对，我们通常说“厕所”或“卫生间”。就在那边。 艾丽斯：好的，我会很快的！我想知道公园今天何时关门。 何伟：九点三十，你不必着急！ SectionA3a 欢乐时光公园——永远快乐的时光 [艾丽斯和何伟在太空世界。] 艾丽斯：我想知道我们接下来应该去哪里？ 何伟：那边那个新项目怎么样？ 艾丽斯：好吧……看起来蛮吓人的。 何伟：快来吧！我保证它将激动人心！如果你害怕，只要大叫或者抓住我的手。 [云霄飞车之后……] 艾丽斯：你是对的！太有趣了！起初我好害怕，但大声喊叫还蛮管用的。 何伟：瞧，那玩意并不糟糕，对吧？某些东西你不去尝试，就绝不会知道。 艾丽斯：对，我很高兴我试过了！ 何伟：你现在想去水上世界么？ 艾丽斯：好，但我很饿。你知道我们在哪里能吃到好的快餐？ 何伟：当然！我建议在水上世界的水城餐馆，那里有美味可口的食物。 艾丽斯：好极了！我们走！ [在前往水城餐馆途中，艾丽斯和何伟经过鲍勃叔叔餐馆。] 艾丽斯：看！这家餐馆看起来蛮有趣的。这招牌上说这儿每晚有摇滚乐队演出。
四种翻译方法 1.直译和意译 所谓直译，就是在译文语言条件许可时，在译文中既保持原文的内容，又保持原文的形式——特别指保持原文的比喻、形象和民族、地方色彩等。 每一个民族语言都有它自己的词汇、句法结构和表达方法。当原文的思想内容与译文的表达形式有矛盾不宜采用直译法处理时，就应采用意译法。意译要求译文能正确表达原文的内容，但可以不拘泥与原文的形式。（张培基） 应当指出，在再能确切的表达原作思想内容和不违背译文语言规范的条件下，直译有其可取之处，一方面有助于保存原著的格调，另一方面可以进新鲜的表达方法。 Literal translation refers to an adequate representation of the original. When the original coincides or almost tallies with the Chinese language in the sequence of vocabulary, in grammatical structure and rhetorical device, literal translation must be used. Free translation is also called liberal translation, which does not adhere strictly to the form or word order of the original.（郭著章） 直译法是指在不违背英语文化的前提下，在英译文中完全保留汉语词语的指称意义，求得内容和形式相符的方法。
九年级英语u n i t课文 翻译 Document serial number【KK89K-LLS98YT-SS8CB-SSUT-SST108】
unit3 Could you please tell me where the restroom are ? sectionA 2d 何伟：这就是欢乐时代公园——我们这座城市最大的游乐园。 爱丽丝：就要玩各种游乐项目了，我好兴奋呀！ 何伟：我们先玩那样呢？有太空世界、水世界、动物世界…. 爱丽丝：在我们决定前，麻烦你先告诉我哪儿有洗手间吗？ 何伟：什么？休息室？你想要休息了？我们可还没有开始玩呢！ 爱丽丝：不是的，我不是指休息的地方。我是说…..你知 道，一间洗手间或卫生间。 何伟：嗯….那么你是指….卫生间吗？ 爱丽丝：对啦！不好意思，也许中国人说英语不常用 restroom这个词。 何伟：就是的，我们常说toilets 或washroom 。不过，厕所在哪里。 爱丽丝：知道了，我一会儿就好！ 何伟：没问题，你不必赶的。 Section A 3a 欢乐时代公园————总是欢乐时光 [ 爱丽丝和何伟在太空世界] 爱丽丝：我不知道我们接下来该去哪里。
何伟：去玩玩那边那个新项目怎样？ 爱丽丝：啊…..看上去挺吓人的。 何伟：勇敢些！我保证会很好玩！如果害怕就喊出来或抓住我的手。 【乘坐后…..】 爱丽丝：你是对的，这真好玩！我起先有些害怕，但喊叫真管用。何伟：瞧：这并不糟糕，对吧？你需要去尝试，否则永远不会知道你能行。 爱丽丝：是这样的，我真高兴自己尝试了这个项目。 何伟：现在你想去水世界吗？ 爱丽丝：当然，但我饿了。你知道哪里有又好吃又快的地方？ 何伟：当然知道！我建议去水世界的水城餐馆他们做得很好吃。爱丽丝：太好了，我们去吧！ 何伟：[在去水城餐馆的路上，爱丽丝与何伟路过鲍勃叔叔的餐厅]爱丽丝：你瞧！这间餐厅看上去很有意思。牌子上写着有个摇滚乐队每晚在演奏。 何伟：我们为何不回头过来在这吃晚饭？咱们去问一下乐队演出几点开始。 【爱丽丝和何伟向门口的员工走去】 爱丽丝：劳驾，请问你们乐队今天晚上何时开始演奏？ 何伟：八点。那时人总是很多，所以得来早一点才有桌子。 爱丽丝：好的，谢谢！
高中英语作文范文赏析 Today, with the development of high-technology, we can get access to all kinds of high-tech products, such as computer, digital cameras and so on. These products make our life more convenient, we can keep in touch with family and friends any time any where. Our life has been changed by the high-tech, we live in a fast-pace world. Cell phone influences our life deeply, everyone owns it. While cell phone brings many dangers. First, cell hone contains radiation which hurts people’s body. Today, more and mo re people die of cancer, the main reason is that the high-tech products radiate their bodies, in the long run, the bodies get sick. Cell phone is one of such products, it hurts our bodies as long we use it. Second, cell phone distracts our attention about discovering the beauty of life. People pay their attention on cell phone, they count on it by reading news and making friends, being less going out. We should use cell phone properly. 今天，随着高科技的发展，我们可以接触各种各样的高科技产品，比如电脑，数字相 机等等。这些产品让我们的生活变得方便，我们可以和家人和朋友随时随地保持联系。我 们的生活受高科技影响而改变，我们生活在一个快节奏的世界。手机深深影响着我们的生活，每个人都有手机。然而手机给我们带来了危害。第一，手机包含了危害我们身体的辐射。现在，越来越多的人死于癌症，主要的原因是高科技产品辐射着他们的身体，长此下去，身体就得病了。手机就是其中的产品，只要我们使用，就会受到危害。第二，手机让 我们忽略了发现生活的美。 As we know, students should learn how to get on well with others. But how? First of all, we should respect others. Everybody has their own way to do things, so we should understand each other. Besides, it’s important for us to communicate with each other and share our happiness and sadness. What’s more, we should be kind to others and offer necessary help to those who are in trouble. If we live in the school’s dormitory, we should be careful not to disturb others. Don’t bring friends back to the dormitory in the mid-night after all the roommates are sleeping. Or playing computer games with the music turn up so loud. Such behaviors will hurt the relationships between you and your roommates. 我们都知道，学生应该学会与人相处。但是该怎样做呢?首先，我们应该相互理解体 谅对方。除此之外，和他人分享我们的喜怒哀乐也是很有必要的。我们还要对他人友善， 为他人提供必要的帮助。如果我们住在学校里面，就要注意不要打扰到他人。不要在午夜 时分舍友睡觉的时，把朋友带回来。或者是大声的开着音乐玩电脑。这种行为会伤害到你 与舍友之间的关系。
英语诗歌以其独特的文体形式充分调动、发挥语言的各种潜能，使之具有特殊的感染力。读来隽永，富有音韵美。下面是是由带来的关于经典英文诗歌，欢迎阅读! 【篇一】关于经典英文诗歌赏析 I Started Early - Took My Dog Emily Dickinson (1830-86) I started Early - Took my Dog And visited the Sea The Mermaids in the Basement Came out to look at me And Frigates - in the Upper Floor Extended Hempen Hands Presuming Me to be a Mouse Aground - upon the Sands But no Man moved Me - till the Tide Went past my simple Shoe And past my Apron - and my Belt And past my Bodice - too And made as He would eat me up As wholly as a Dew Upon a Dandelion's Sleeve And then - I started - too And He - He followed - close behind I felt His Silver Heel Upon my Ankle - Then my Shoes
Would overflow with Pearl Until We met the Solid Town No One He seemed to know And bowing - with a Mighty look At me - The Sea withdrew 【篇二】关于经典英文诗歌赏析 The Wild Swans At Coole William Butler Yeats (1865-1939) The trees are in their autumn beauty, The woodland paths are dry, Under the October twilight the water Mirror a still sky; Upon the brimming water among the stones Are nine-and-fifty swans. The nineteenth autumn has come upon me Since I first made my count; I saw, before I had well finished, All suddenly mount And scatter wheeling in great broken rings Upon their clamorous wings. I have looked upon those brilliant creatures, And now my heart is sore. All's changed since I, hearing at twilight, The first time on this shore,
一.用词准确;表达地道 【北京卷】【试题回放】第一节情景作文(20分) 美国中学生jeff将要来你所在的红星中学学习中文，经协商安排住在你家。假设你是李华，请给Jeff写一封信，按照下图顺序介绍他来中国后的生活安排。 注意：1. 信的开头已为你写好。 2.词数不少于60。 Dear Jeff, I’m Hua from Beijing Hongxing Middle School. I’m very happy to learn that you’re going to stay with my family while you’re in Beijing. While you are here, we’ll provide you with a room of your own with a bed, a desk, a couple of chairs and a TV. You’ll also have your own bathroom. Our school is quite close to our home, so we could go to school t ogether by bike. At noon we’ll eat at the school dining hall. I’m sure you’ll like the delicious Chinese food there, and enjoy talking with friends over lunch. Classes in our school usually finish at 4 in the afternoon. You can then join other students in playing ball games or swimming. It’ll be a lot of fun. If you have any questions or requests, please let me know. We’ll try our best to make your stay here in Beijing a pleasant experience. Best wishes, Li Hua [名师点评]
高一英语翻译技巧和方法完整版及练习题及解析 一、高中英语翻译 1．高中英语翻译题：Translation: Translate the following sentences into English, using the words given in the brackets. 1．究竟是什么激发小王学习电子工程的积极性？(motivate) 2．网上支付方便了客户，但是牺牲了他们的隐私。(at the cost of) 3．让我的父母非常满意的是，从这个公寓的餐厅可以俯视街对面的世纪公园，从起居室也可以。(so) 4．博物馆疏于管理，展品积灰，门厅冷落，急需改善。(whose) 【答案】 1．What on earth has motivated Xiao Wang’s enthusiasm/ initiative to major in electronic engineering? 2．Online payment brings convenience to consumers at the cost of their privacy. 3．To my parents’ satisfaction, the dining room of this apartment overlooks the Century Park opposite the street and so it is with the sitting room. 或者What makes my parents really satisfy is that they can see the Century Park from the dining room of this apartment, so can they from the living room. 4．This museum is not well managed, whose exhibits are covered with dust, and there are few visitors, so everything is badly in need of improvement. 或The museum whose management is reckless, whose exhibits are piled with dust and whose lobby is deserted, requires immediate improvement. 【解析】 1．motivate sb to do sth 激发某人做某事，on earth究竟，major in 以…为专业，enthusiasm/ initiative热情/积极性，故翻译为What on earth has motivated Xiao Wang’s enthusiasm/ initiative to major in electronic engineering? 2．online payment网上支付，brings convenience to给…带来方便，at the cost of以…为代价，privacy隐私，故翻译为Online payment brings convenience to consumers at the cost of their privacy. 3．To my parents’ satisfaction令我父母满意的是，后者也那样so it is with。也可以用主语从句What makes my parents really satisfy 表语从句thatthey can see the Century Park from the dining room of this apartment。overlooks俯视，opposite the street街对面，living room 起居室。故翻译为To my parents’ satisfaction, the dining room of this apartment overlooks the Century Park opposite the street and so it is with the sitting room.或者What makes my parents really satisfy is that they can see the Century Park from the dining room of this apartment, so can they from the living room. 4．not well managed/ management is reckless疏于管理，be covered with dust/ be piled with dust被灰尘覆盖，few visitors游客稀少，be badly in need of improvement/ requires immediate improvement亟需改善。故翻译为his museum is not well managed, whose exhibits
英语新课标九年级课文翻译Unit9-14 Unit9 I like music that I can dance to. SectionA 2d 吉尔:斯科特,周末你打算干什么呢? 斯科特:没什么事,我估计就是听听我新买的激光唱片吧. 吉尔:哦?是什么激光唱片? 斯科特:嗯,全是音乐的,没有歌曲。我喜欢听舒缓的音乐来放松自己,尤其是在工作了漫长的一周以后。 吉尔:听起来不错啊。嗯,如果你有空,愿意和我一起去看部电影吗?(电影的)导演很有名。 斯科特:嗯,那要看什么电影。我只喜欢有趣的电影,我只想笑一笑不想费脑筋,你懂我的意思吧? 吉尔:哦,那样的话,我还是去邀请喜欢看严肃电影的人吧. 斯科特:(你说的)电影是关于什么的? 吉尔:是关于第二次世界大战的。我喜欢能让我思考的电影。 section A, 3a 今天你想看什么(电影)呢? 虽然一些人坚持只看一种电影,但是我喜欢看不同种类的电影,(具体)由当时盼心情决定。 当我情绪低落或感到疲惫的时候,我更喜欢能让我开心的影片。比如,像《黑衣人》那样的喜剧片或像《功夫熊猫》这类的动画片,通常都有滑稽的对话和一个愉快的结局。影片中的人物不一定完美,但是他们都会尽力去解决问题,看了这样的电影,我所面对的许多问题突然间会显得不那么严重,我也会感觉好多了。两个小时的欢笑是一种很好的放松方式。 当我伤心或劳累的时候,我不看剧情片或纪录片。像《泰坦尼克号》这样的剧情片只会让我更伤心。像《帝企鹅日记》这样的纪录片,(通常)会针对某个特定话题提供丰富的信息,(内容)也很有趣,但是当我累的时候,我不想思考太多。当我太累不想思考时,我不介意看像《蜘蛛侠》这样的动作电影。我只想屏蔽我的大脑,坐在那里观看一个令人兴奋的超级英雄,他总是能在关键时刻挽救世界。 偶尔我会喜欢看恐怖片。虽然它们很有意思,但是我会因为太害怕而不敢独自一人看,我总会带上一位不怕这些类型的电影的朋友(一起看),这样就觉得没那么可怕了。 Secton B 2b 凄美 昨晚我的一个中国朋友带我去听了一场中国民间音乐会。其中有一首二胡曲令我特别感动。音乐出奇的美,但是在那美的背后,我感受到悲伤和痛苦。这首曲子有个简单的名字,《二泉映月》,但它是我听到过的最感人的曲子之一。二胡(的声音)听起来那么悲伤,以至于我在听的时候也几乎随着它哭了。后来我查阅了《二泉映月》的历史,开始理解音乐中蕴含的伤感。 这首曲子由一位民间音乐家阿炳写成,他于1893年出生在无锡市。在他还很小的时候,他的母亲就去世了。阿炳的父亲教他弹奏各种乐器,如鼓、笛子和二胡。到了十七岁,阿炳就以他的音乐天赋闻名。然而,他的父亲去世后,阿炳的生活变得更糟糕。他很穷,还得了很严重的疾病,眼睛瞎了。好些年他都没有家,他住在大街上,以弹奏音乐来谋生。即使在他结了婚有了家以后,他还是继续在街道上唱歌、弹曲,他以这种方式表演了好多年。 阿炳惊人的音乐技能让他在有生之年就非常出名。到他临终前,他已会弹六百多首曲子,大部分是他自己写的。遗憾的是,一共只有六首曲子被录了下来得以传世,但时至今日,他(的作品)依旧颇受人们喜爱。今天,阿炳的《二泉映月》成 了所有伟大的二胡演奏家弹奏和赞赏的曲子。它已成了中国文化魁宝之一。它的凄美不仅描绘出阿炳自己的生活,而且也让人们回想起自身的悲苦体验和最深的的痛。
英文诗歌赏析方法 英诗的欣赏：诗的格律、诗的押韵、诗的体式、诗的评判。 诗以高度凝结的语言表达着人们的喜怒哀乐，用其特有的节奏与方式影响着人们的精神世界。诗讲究联想，运用象征、比喻、拟人等各种修辞手法，形成了独特的语言艺术。 一、诗的格律 “格律是指可以用脚打拍子的节奏”，是每个音步轻重音节排列的格式，也是朗读时轻重音的依据。而音步是由重读音节和非重读音节构成的诗的分析单位。重读音节为扬（重），在音节上用“－”或“?”标示，非重读音节为抑（轻），在音节上用“?”标示，音步之间可用“／”隔开。以下是五种常见格式： 1. 抑扬格（轻重格）Iambus：是最常见的一种格式，每个音步由一个非重读音节加一个重读音节构成。 As fair / art thou / my bon/nie lass， So deep / in luve / am I ： And I / will luve / thee still，/ my dear，Till a` / the seas / gang dry： Robert Burns（1759-1796）：My Luve Is like a Red，Red Rose 注；art=are luve=love bonnie=beautiful a`=all gang=go 上例中为四音步与三音步交叉，可标示为：?－／?－／?－／（?－） 2.扬抑格（重轻格）Trochee：每个音步由一个重读音节加一个非重读音节构成。 下例中为四音步扬抑格（少一个轻音节），可标示为：－?／－?／－?／－ Tyger！/ Tyger！/ burning / bright In the / forests / of the / night William Blake：The Tyger 3. 抑抑扬格（轻轻重格）Anapaestic foot：每个音步由两个非重读音节加一个重读音节构成。如：三音步抑抑扬格??－／??－／??－ Like a child / from the womb， Like a ghost / from the tomb， I arise / and unbuild / it again. 4. 扬抑抑格（重轻轻格）Dactylic foot：每个音步由一个重读音节加两个非重读音节构成。如：两音步扬抑抑格－??／－?? ?Touch her not / ?scornfully， ?Think of her / ?mournfully. - Thomas Hood 5. 抑扬抑格（轻重轻格）Amphibrach：每个音步由一个非重读音节加一个重读音节再加一个非重读音节构成。如：三音步抑扬抑格?－?／?－?／?－?下例中最后一个音步为抑扬格。 O ?hush thee / my ?babie / thy ?sire was / a knight. 在同一首诗中常会出现不同的格律，格律解析对朗读诗歌有一定参考价值。现代诗中常不遵守规范的格律。 二、诗的押韵
文言文翻译技巧和方法 一、基本方法：直译和意译文言文翻译的基本方法有直译和意译两种。所谓直译，是指用现代汉语的词对原文进行逐字逐句地对应翻译，做到实词、虚词尽可能文意相对。直译的好处是字字落实;其不足之处是有时译句文意难懂，语言也不够通顺。所谓意译，则是根据语句的意思进行翻译，做到尽量符合原文意思，语句尽可能照顾原文词义。意译有一定的灵活性，文字可增可减，词语的位置可以变化，句式也可以变化。意译的好处是文意连贯，译文符合现代语言的表达习惯，比较通顺、流畅、好懂。其不足之处是有时原文不能字字落实。这两种翻译方法当以直译为主，意译为辅。 二、具体方法：留、删、补、换、调、变。 “留”：就是保留。凡是古今意义相同的词，以及古代的人名、地名、物名、官名、国号、年号、度量衡单位等，翻译时可保留不变。例如：《晏子使楚》中的“楚王”、“晏婴”、“晏子”等不用翻译。 “删”，就是删除。删掉无须译出的文言虚词。例如：“寡人反取病焉”的“焉”是语气助词，可不译，本句的意思就是“我反而自讨没趣。”(《晏子使楚》)又如：“子猷、子敬俱病笃，而子敬先亡”中的“而”是连词，可不译，整句意思是“子猷与子敬都病重，子敬先死去。” “补”，就是增补。(1)变单音词为双音词，如《桃花源记》中“率妻子邑人来此绝境”，“妻子”一词是“妻子、儿女”的意思;(2)补出省略句中的省略成分，如《人琴俱亡》中“语时了不悲”，翻译为：(子猷)说话时候完全不悲伤。 “换”，就是替换。用现代词汇替换古代词汇。如把“吾、余、予”等换成“我”，把“尔、汝”等换成“你”。“调”就是调整。把古汉语倒装句调整为现代汉语句式。例如《人琴俱亡》中“何以都不闻消息”，“何以”是“以何”的倒装，宾语前置句，意思是“为什么”。“变”，就是变通。在忠实于原文的基础上，活译有关文字。“子猷问左右”(人琴俱亡))中的“左右”指的是“手下的人”，“左右对曰”(《晏子使楚》中的“左右”指的是“近臣”。 古文翻译口诀古文翻译，自有顺序，首览全篇，掌握大意；先明主题，搜集信息，由段到句，从句到词，全都理解，连贯一起，对待难句，则需心细，照顾前文，联系后句，
7楼 迪士尼乐园是个娱乐的公园，但我们也可以叫它“主题公园”。它拥有你在其他公园可以找到的所有的娱乐设施，但是它有一个主题。当然，这个主题就是迪士尼电影和迪士尼人物。比如说，在其他一些公园你可以看到到摩天轮，但是在迪士尼乐园，摩天轮就有了“迪士尼人物”的主题。这意味着你可以在摩天轮的任何地方看到迪士尼人物。同样，你也可以看有关迪士尼的电影，在迪士尼餐厅就餐，买迪士尼礼物。你还随时可以看到迪士尼乐园里来回走动的迪士尼人物！ 你听说过“迪士尼航行”吗？那是同样有迪士尼主题的巨大的船。你可以在船上航行几天，还可以在甲板上吃东西睡觉。和迪士尼乐园一样，甲板上也有许多吸引人的地方。你可以购物，参加迪士尼的聚会，和米老鼠一起吃晚餐。这些船有几条不同的航线，但最终都会抵达同样的地方。那就是属于迪士尼乐园的小岛。 在迪士尼乐园的乐趣简直太多了！ 9. p72 UNIT 9 3a: Come to the Hilltop Language School and change your life. 来到Hilltop语言学校,改变你的人生! 第一篇:这里是两名同学讲述关于我校的事情 当我还是个小女孩,我就梦想着去旅行,因而我选择了个最佳的方式—从事空中乘务员.我做这个行业已有两年了,它的确是份有趣的工作,我能游遍世界各地,但也我发现说好英语对我来说是件多么重要的事,正因如此早在当空乘之前我就在Hilltop语言学校学习五年了,我以一口流利的口语赢得了这份工作,谢谢, Hilltop语言学校! Mei Shan 第二篇: 我渴望当一名导游,事实上,这是我一直都很想要从事的事业.我渴望旅行,特别是英语国家,像是美国,澳大利亚.不论如何我知道我必须提高我的英语能力,于是我来到Hilltop语言学校进行口语学习, Hilltop语言学校对我的学习有很大的帮助,我已经在这里学满一年了,非常热爱这个地方.或许当我要离开这个学校的时候,我开始想做一名英语教师的热情会大过于想做一名导游! David Feng 9. p74 UNIT 9 3a: Have you ever been to Singapore？翻译！ 你去过新加坡吗？ 对于很多中国旅游者来说，这个位于东南亚的小岛是个度假的好去处。一方面，超过四分之
经典英文诗歌赏析(全) 一 nothing gold can stay 1简介：《美景易逝(Nothing Gold Can Stay)》罗伯特弗罗斯特 的代表作之一。此诗于1923年写就，即于当年十月在《耶鲁杂志(The Yale Review)》上刊印出版，随后就被收录到弗罗斯特的一本名为 《新罕布什尔州(New Hampshire)》的诗集中。 2诗歌翻译： Nothing gold can stay 岁月留金 Nature's first green is gold, 大自然的第一抹新绿是金， Her hardest hue to hold. 也是她最无力保留的颜色.。 Her early leaf's a flower; 她初发的叶子如同一朵花,; But only so an hour. 不过只能持续若此一刹那。 Then leaf subsides leaf, 随之如花新叶沦落为旧叶。 So Eden sank to grief. 由是伊甸园陷入忧伤悲切， So down gose down to day, 破晓黎明延续至晃晃白昼。 Nothing gold can stay. 宝贵如金之物岁月难保留。 3诗歌赏析：这首诗揭示了一切真切而美好的事物最终定会逐渐消失的哲理。它同时也使用了独特的技巧来表现了季节的变化。想到了 小时了了，大未必佳。一切都是转瞬即逝的，浮世有的仅仅转丸般的 繁华。 二 the road not taken 1诗歌简介：这首名诗《The Road NotTaken》形式是传统的抑扬 格四音步，但音步可变(含有很多抑抑扬的成分);每节的韵式为abaab 。
英语优秀范文赏析 一.父亲节马上就要到了，但是有些同学不知道送什么礼物给父亲。请根据下面的提示进行适当扩展，并向同学们提出一些建议。80词左右，开头和结尾以给出（不计入总词数）。 提示：1.如果有足够的零花钱，可以为父亲买一些使用单不贵的东西，如领带等： 2.还可以为父亲做些力所能及的事情，如为父亲准备一杯茶 等他下班后饮用等。 Father’s Day is coming and you must be thinking of giving a present to your father. Different people like different kinds of gifts. If you have enough pocket money, you can buy a useful but not expensive thing, like a tie. I think your father will like it. But if you don’t have enough pocket money, you can do something that you can do.For example, you can prepare a cup of tea. When your father comes back from work, he can drink it. No matter what you do, the most important thing is to make your father happy on Father’s Day. Don’t you think so? 二.请根据提示以“The Spring Festival”为题，写一篇不少于80词的英语短文。 提示：1.春节是中国最重要的节日； 2.人们大多回家过年，家庭成员团聚； 3.家人一起吃团年饭、看电视、拜访亲朋好友（friends and relatives）; 4.孩子们喜欢春节。 The Spring Festival The Spring Festival comes in wenter. It is the most important traditional festival in China.
人教版九年级英语课文翻译 一单元 SECTION A 1a 我通过制作抽认卡来学习。通过和朋友一起学习。通过听磁带。通过做抽认卡。通过向老师求助。通过读课本。通过制作单词本。 1c A：你怎么为考试而学习。B：我通过参加学习小组来学习。 2a 1、你是通过看英文录像学英语的吗？ 2、你曾和朋友们练习过对话吗？ 3、听磁带怎么样？ 4、大声朗读以练习发音怎么样？5、我曾经通过参加学习小组的方式学习过吗？ 2b A是的，我通过那种学习方式学到了很多。B、哦，是的，它提高了我说英语的能力。C、有时那样做。我觉得他有用。D、不。（通过看英语录像学习）太难了，无法理解录像中的人所说的话。 2c A你曾经通过参加学习小组来学习吗？B、是的，我参加赤字，通过那种方式我学到了很多。 Grammer Focus 你怎么为准备一场考试而学习？我靠听磁带。你怎样学习英语？我通过参加学习小组来学习。你通过大声朗读来学习英语吗？是的，我是。你曾和朋友们练习过对话吗？哦，是的，他提高了我说英语的能力。你曾经通过参加学习？小组来学习吗？是的，我参加过。通过那种方式我学习到了很多。 3a如何才能学得最好 这星期我们询问了新星高中的同学关于学习更多英语的最佳方法的问题。许多同学说他们通过使用英语为学习它，一些还有很特别的建议。比如，李莉莲说学习新单词的最好的方法是阅读英语杂志。她说记忆浒音乐的歌词也有一些作用。当我们问及学习语法的问题时，她说：“我从不学习语法。它太枯燥了。” 魏明有不同的看法。他学习英语已经6年了，并且确实喜欢英语。他认为学习语法是学习一门语言的一种好方法。他还认为观看英语电影也不错，国灰他可以看到演员说话的情形。但是，有时候他发现看英语电影是件很头痛的事情，因为那些演员说话太快了。 刘畅说加入学校英语俱乐部是提高英语最好的方法。学生有很多练习的机会并且他们也有很多乐趣。她补充说和朋友练习会话一点用处也没有。“我们会因为某件事变得很激动，最后用汉语来讲，”她说。 3b A：我正在作一个关于学习英语的调查。我能问你一些问题吗？B：当然。A：太好了！你叫什么名字？B：魏明。A：那么你是怎样学习英语的，魏明？B：…… 4 A：你列词汇表吗？B：噢，是的。我常那样做。 SECTION B 1a我不会发其中一些单词的音。我不会拼写一些英语单词。我听不懂英语口语。我在语法上犯错误。我读得很慢。1b我不知道怎么使用逗号。 2a 1、不能正确发音。 2、忘记很多生词。 3、人们和我说话时我不能每次都听懂。 4、不能理解杂志中的单词。 5、没有获得很多写作训练。 2B A、你可以一直将生词写在你的笔记本里，并在家学习它们。B、你应该找一个笔友。C、听力能起作用。D、为什么不加入一个英语俱乐部来练习说英语呢？ 2C A：我没有搭档来练习英语。B、也许我应该加入一个英语俱乐部。 3a我是怎样学习英语的 去年英语课对我来说很难。首先，对我来说听懂老师说话很难。开始，她说的太快，我不能听懂每个单词，后来，我意识到如果你听不懂每个单词并没有关系。而且我害怕在班上说话，因为我认为同学们可能会嘲笑我。我也不是总能造出完整的句子。然后我开始看英文电视。那很有用。我认为做大量听力练习是成为一个好的语言学习者的秘决之一。另一件我觉得很难的事是英语语法。所以我决定在每节课上记大量语法要点。然后我开始用我正在学的语法自己写新句子。这样作用处之大令人惊奇。现在我很喜欢学英语并且这学期我得了个A。我的老师对我印象很深。作者觉学英语很难是因为……1、老师发音差。2、她说话时人们总是嘲笑她。3、她在造完整的句子方面有困难。4、英语语法很难。当她开始…她的英语提高了。5、和说英语的朋友一起出去。6、大量的听力练习。7、在自己组织的句子里使用语法。 3b 亲爱的，我知道学英语不容易，但我有一些想法可能有用。你说你不能理解说话太快的人。那么，你可以尽量听最重要的单词，而不是每个单词。 4 1、关于学英语什么不容易。2、就这一点你作了什么？3、你最喜欢的学习更多英语的方式是什么？韩文说如果人
The Basic Elements of Appreciating English Poetry is poetry Poetry is the expression of Impassioned feeling in language. “Poetry is the spontaneous overflow of powerful feelings: it takes its origin from emotion recollected in tranquility.” “Poetry, in a general sense, may be defined to be the expression of the imagination.”Poetry is the rhythmical creation of beauty. Poetry is the image of man and nature. ~ “诗言志，歌咏言。” ---《虞书》 “诗言志之所以也。在心为志，发言为诗。情动于中而行于言，言之不足，则嗟叹之；嗟叹之不足，故咏歌之；咏歌之不足，不知手之舞之，足之蹈之也。情发于声；声成文，谓之音。” ---《诗·大序》 “诗是由诗人对外界所引起的感觉，注入了思想与情感，而凝结了形象，终于被表现出来的一种‘完成’的艺术。” ---艾青：《诗论》 Sound System of English Poetry a. The prosodic features Prosody (韵律)---the study of the rhythm, pause, tempo, stress and pitch features of a language. Chinese poetry is syllable-timed, English poetry is stress-timed. Stress: The prosody of English poetry is realized by stress. One stressed syllable always comes together with one or more unstressed syllables. eg. Tiger, /tiger, /burning /bright — In the /forest /of the/ night, What im/mortal /hand or /eye Could frame thy/ fearful /symme/try ---W. Blake Length: it can produce some rhetorical and artistic effect. eg. The curfew tolls the knell of parting day, The lowing herd wind slowly o’er the lea, The Ploughman homeward plods his weary way, And leaves the world to darkness and to me. ---Thomas Gray Long vowels and diphthongs make the poem slow, emotional and solemn; short vowels quick, passionate, tense and exciting. Pause: it serves for the rhythm and musicality of poetry.