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1、 One-and two-dimensional Anderson model with long-range correlated-disorderAnderson model-IntroductionEntanglement in 1D2D Entanglement2D conductance2D transmission2D magnetoconductance第1页/共25页Anderson model-IntroductionWhat is a disordered system?No long-range translational orderTypes of disorder (
2、a)crystal(a)crystal(b)Component(b)Component disorderdisorder(c)position(c)position disorderdisorder(d)topological(d)topologicaldisorderdisorder第2页/共25页 diagonal disorder off-diagonal disorder complete disorder Localization prediction：an electron,when placed in a strong disordered lattice,will be imm
3、obile 1 P.W.Anderson,Phys.Rev.109,1492(1958).Anderson model-IntroductionBy P.W.Anderson in 19581第3页/共25页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 w
4、ork,Tal Schwartz et al.realized the Anderson localization with disordered two-dimensional photonic lattices2.1John S,Sompolinsky H and Stephen M J 1983.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 52第4页/共2
5、5页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).第5页/共25页Results of J.J.Lin in 19872dephasing time第6页/共25页Work of Hui Xu et al.on systems with correlated disorder:刘小良，徐慧，等，物理学报，55(5)，2493
7、（2006）；刘小良，徐慧，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）。第7页/共25页Anderson model-new points of view1。Correlated disorderCorrelation and disorder are two of the most important concepts in solid state physi
8、csPower-law correlated 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 dow
9、nEntanglement of spatial 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.Inform.4,705(2006).Hefeng Wang and Sabre K
10、ais,Int.Inform.4,827(2006).第8页/共25页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,2
11、D Anderson system1R.G.Endres,D.L.Cox and R.R.P.Singh,Rev.Mod.Phys.76,195(2004)；Stephan Roche,.91,108101(2003).2 and,Synthetic Metals,139(2003)239-244;J.Cornil,J.Ph.Calbert and,J.Am.Chem.Soc.,123,1520-1521(2001).DNA structure第9页/共25页Entanglement in one-dimensional Anderson model with long-range corre
12、lated disorder one-dimensional nearest-neighbor tight-binding model Concurrence:von Neumann entropy 第10页/共25页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 concurre
13、nce of 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 第11页/共25页2D entanglementMethod:taking the 2D lattice as 1D chain1 Longyan Gong and Peiqing Tong,Phys.Rev.E 74(2006)056103.；Phys.Rev.A 71,042333(2005).Quant
14、um small world network in 1 square lattice第12页/共25页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 correlati
15、on as the function of disorder degree W and for various .A band structure is demonstrated.第13页/共25页Lonczos method第14页/共25页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 inflat
16、ion(substitutions)rule is GGC;CGA;ATC;TTA.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 generation
17、s are 1,2,4,8,16,and for the12th generation,the site number is 2048.第15页/共25页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.第16页/共25页Spin Entanglement of non-interacting multiple
18、particles:Greens function methodFinite temperature two body Greens functionFinite temperature two body Greens functionOne particle density matrix and One body Greens functionOne particle density matrix and One body Greens functionTwo particle density matrixTwo particle density matrixwhere,HF approx.
19、第17页/共25页 Ifandwhere&whereGeneralized Werner StatethenInbasisSeparability criterion=PPT=always satisfied since第18页/共25页Conductance and magnetoconductance of the Anderson model with long-range correlated disorder(1)Static conductance of the two-dimensional quantum dots with long-range correlated diso
20、rder Idea:the distribution function of the conductance in the localized regime1d:clear Gaussian2d:unclearMethod to calculating the conductance:Greens function and Kubo formula第19页/共25页第20页/共25页Fig.1 Conductance as the function of Fermi energy for the systems with power-law correlated disorder(W=1.5)
21、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 different Fermi energies(a)Gaussian correlated disor
22、der,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第21页/共25页(2)Transmittance of the two-dimensional quantum dot systems with Gaussian correlated disorder Effects of leads第22页/共25页(3)magnetoconductance Related with quantum chaos第23页/共25页Thank you!第24页/共25页感谢您的观看！第25页/共25页