一维和二维关联无序安德森模型.ppt

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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-disorder Anderson model-Introduction Entanglement in 1D 2D Entanglement 2D conductance 2D transmission 2D magnetoconductance,Anderson model-

2、Introduction What is a disordered system? No long-range translational order Types of disorder,(a)crystal,(b) Component disorder,(c) position disorder,(d) topological disorder,diagonal disorder off-diagonal disorder complete disorder Localization prediction：an electron, when placed in a strong disord

3、ered lattice, will be immobile 1 P.W.Anderson, Phys.Rev.109 ,1492(1958).,Anderson model-Introduction By P.W.Anderson in 19581,Anderson model-Introduction In 1983 and 1984 John extended the localization concept successfully to the classical waves, such as elastic wave and optical wave 1. Following th

4、e previous experimental work ,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 Phys.Rev.Lett. 53 2169 2Schwartz Tal, Bartal Guy, Fi

5、shman Shmuel and Segev Mordechai 2007 Nature 446 52,Anderson model-open problems Abrahans 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

6、experiments in early 1980s. （2） （dephasing time ） Results of J.J.Lin in 19872,1 E.Abrahans,P.W.Anderson, D.C.Licciardello and T.V. Ramakrisbnan, Phys.Rev.Lett. 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).,Res

7、ults 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

8、-new points of view 1。Correlated disorder Correlation and disorder are two of the most important concepts in solid state physics Power-law correlated disorder Gaussian correlated disorder 2。Entanglement1：an index for metal-insulator,localization-delocalization transition ”entanglement is a kind of u

9、nlocal correlation”（MPLB19,517,2005）. Entanglement of spin wave functions:four states in one site:0 spin; 1up; 1down; 1 up and 1 down Entanglement of spatial wave functions (spinless particle) :two states:occupied or unoccupied Measures of entanglement：von Newmann entropy and concurrence 1Haibin Li

10、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.Quant. Inform.4 , 827(2006).,Anderson model- new points of view 3.new applications （1）quantum chaos （2）electron transport in DNA

11、 chains The importance of the problem of the electron transport in DNA1 （3）pentacene2（并五苯） Molecular electronics Organic field-effect-transistors pentacene:layered structure, 2D Anderson system 1R. G. Endres, D. L. Cox and R. R. P. Singh,Rev.Mod.Phys.76 ,195(2004)； Stephan Roche, Phys.Rev.Lett. 91 ,

12、108101(2003). 2 M.Unge and S.Stafstrom, Synthetic Metals,139(2003)239-244;J.Cornil,J.Ph.Calbert and J.L.Bredas, J.Am.Chem.Soc.,123,1520-1521(2001).,DNA structure,Entanglement in one-dimensional Anderson model with long-range correlated disorder one-dimensional nearest-neighbor tight-binding model Co

13、ncurrence:,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 the Anderson model with power-law correlation for =3.0 and at the bi

14、gger W range. A jumping from the upper band to the lower band is shown,2D entanglement Method: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 network in 1 square lattice,Left. The average concurrence of t

15、he 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 disorder degree W and for various . A band structure is dem

16、onstrated.,Lonczos method,Entanglement in DNA chain guanine (G), adenine (A), cytosine(C), thymine (T) Qusiperiodical model R-S model to generate the qusiperiodical sequence with four elements (G,C,A,T) .The inflation(substitutions) rule is GGC;CGA;ATC;TTA. Starting with G (the first generation), th

17、e 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 generation , the site number is 2048.,Th

18、e 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 body Greens function,One parti

19、cle 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-dimensional quantum dots with long-ran

20、ge correlated disorder Idea:the distribution function of the conductance in the localized regime 1d:clear Gaussian 2d: unclear Method 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 systems with power-law

21、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 different Ferm

22、i 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 !,