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1、One-and two-dimensional Anderson model with long-range correlated-disorder一维和二维关联无序安德森模型,One-and two-dimensional Anderson model with long-range correlated-disorderAnderson model-IntroductionEntanglement in 1D2D Entanglement2D conductance2D transmission2D magnetoconductance,Anderson model-Introductio
2、nWhat is a disordered system?No long-range translational orderTypes of disorder,(a)crystal,(b)Component disorder,(c)position disorder,(d)topologicaldisorder,diagonal disorder off-diagonal disorder complete disorder Localization prediction：an electron,when placed in a strong disordered lattice,will b
3、e immobile 1 P.W.Anderson,Phys.Rev.109,1492(1958).,Anderson model-IntroductionBy P.W.Anderson in 19581,Anderson model-IntroductionIn 1983 and 1984 John extended the localization concept successfully to the classical waves,such as elastic wave and optical wave 1.Following the previous experimental wo
4、rk,Tal Schwartz et al.realized the Anderson localization with disordered two-dimensional photonic lattices2.1John S,Sompolinsky H and Stephen M J 1983 Phys.Rev.B27 5592;John S and Stephen M J 1983 28 6358;John S 1984.53 21692Schwartz Tal,Bartal Guy,Fishman Shmuel and Segev Mordechai 2007 Nature 446
5、52,Anderson model-open problemsAbrahans et al.s scaling theory for localization in 19791（3000 citations，one of the most important papers in condensed matter physics）Predictions（1）no metal-insulator transition in 2d disordered systems Supported by experiments in early 1980s.（2）（dephasing time）Results
6、 of J.J.Lin in 19872,1,and T.V.Ramakrisbnan,.42,673(1979)2 J.J.Lin and N.Giorano,Phys.Rev.B 35,1071(1987);J.J.Lin and J.P.Bird,J.Phys.:Condes.Matter 14,R501(2002).,Results of J.J.Lin in 19872,dephasing time,Work of Hui Xu et al.on systems with correlated disorder:刘小良，徐慧，等，物理学报，55(5)，2493（2006）；刘小良，徐
7、慧，等，物理学报，55(6)，2949（2006）；徐慧,等，物理学报，56(2)，1208（2007）；徐慧,等，物理学报，56(3)，1643（2007）；马松山，徐慧，等，物理学报，56(5)，5394（2007）；马松山，徐慧，等，物理学报，56(9)，5394（2007）。,Anderson model-new points of view1。Correlated disorderCorrelation and disorder are two of the most important concepts in solid state physicsPower-law correla
8、ted disorder Gaussian correlated disorder 2。Entanglement1：an index for metal-insulator,localization-delocalization transition”entanglement is a kind of unlocal correlation”（MPLB19,517,2005）.Entanglement of spin wave functions:four states in one site:0 spin;1up;1down;1 up and 1 downEntanglement of sp
9、atial wave functions(spinless particle):two states:occupied or unoccupiedMeasures of entanglement：von Newmann entropy and concurrence1Haibin Li and Xiaoguang Wang,Mod.Phys.Lett.B19,517(2005)；Junpeng Cao,Gang Xiong,Yupeng Wang,X.R.Wang,Int.J.Quant.Inform.4,705(2006).Hefeng Wang and Sabre Kais,Int.J.Q
10、uant.Inform.4,827(2006).,Anderson model-new points of view3.new applications（1）quantum chaos（2）electron transport in DNA chainsThe importance of the problem of the electron transport in DNA1（3）pentacene2（并五苯）Molecular electronicsOrganic field-effect-transistorspentacene:layered structure,2D Anderson
11、 system1R.G.Endres,D.L.Cox and R.R.P.Singh,Rev.Mod.Phys.76,195(2004)；Stephan Roche,.91,108101(2003).2 M.Unge and S.Stafstrom,Synthetic Metals,139(2003)239-244;J.Cornil,J.Ph.Calbert and,J.Am.Chem.Soc.,123,1520-1521(2001).,DNA structure,Entanglement in one-dimensional Anderson model with long-range co
12、rrelated disorder one-dimensional nearest-neighbor tight-binding model Concurrence:,von Neumann entropy,Left.The average concurrence of the Anderson model with power-law correlation as the function of disorder degree W and for various.A band structure is demonstrated.Right.The average concurrence of
13、 the Anderson model with power-law correlation for=3.0 and at the bigger W range.A jumping from the upper band to the lower band is shown,2D entanglementMethod:taking the 2D lattice as 1D chain,1 Longyan Gong and Peiqing Tong,Phys.Rev.E 74(2006)056103.；Phys.Rev.A 71,042333(2005).,Quantum small world
14、 network in 1 square lattice,Left.The average concurrence of the Anderson model with power-law correlation as the function of disorder degree W and for various.A band structure is demonstrated.Right.The average von Newmann entropy of the Anderson model with power-law correlation as the function of d
15、isorder degree W and for various.A band structure is demonstrated.,Lonczos method,Entanglement in DNA chain guanine(G),adenine(A),cytosine(C),thymine(T)Qusiperiodical modelR-S model to generate the qusiperiodical sequence with four elements(G,C,A,T).The inflation(substitutions)rule is GGC;CGA;ATC;TT
16、A.Starting with G(the first generation),the first several generations are G,GC,GCGA,GCGAGCTC,GCGAGCTC GCGATAGA.Let Fi the element(site)number of the R-S sequence in the ith generation,we have Fi+1=2Fi for i=1.So the site number of the first several generations are 1,2,4,8,16,and for the12th generati
17、on,the site number is 2048.,The average concurrence of the Anderson model for the DNA chain as the function of site number.The results are compared with the uncorrelated uniform distribution case.,Spin Entanglement of non-interacting multiple particles:Greens function method,Finite temperature two b
18、ody Greens function,One particle density matrix and One body Greens function,Two particle density matrix,where,HF approx.,If,and,where,Generalized Werner State,then,Conductance and magnetoconductance of the Anderson model with long-range correlated disorder,(1)Static conductance of the two-dimension
19、al quantum dots with long-range correlated disorder Idea:the distribution function of the conductance in the localized regime1d:clear Gaussian2d:unclearMethod to calculating the conductance:Greens function and Kubo formula,Fig.1,Fig.2a,Fig.2b,Fig.1 Conductance as the function of Fermi energy for the
20、 systems with power-law correlated disorder(W=1.5)for various exponent.The results are compared to the reference of that of a uniform random on-site energy distribution.solid:uniform distribution reference;dash:;dash dot:;dash dot dot:;short dash:Fig.2 Conductance changes with disorder degree for di
21、fferent Fermi energies(a)Gaussian correlated disorder,solid:Ef=0;dash:Ef=1.5;short dash:Ef=-1.5;dash dot dot:Ef=2.5;dot:Ef=-2.5(b)power-law correlated disorder,solid:Ef=0;dash:Ef=1.5;dot:Ef=2.5(c)disorder with uniform distribution,solid:Ef=0;dash:Ef=1.5;dot:Ef=2.5,(2)Transmittance of the two-dimensional quantum dot systems with Gaussian correlated disorder Effects of leads,(3)magnetoconductance,Related with quantum chaos,Thank you!,
