Quantum continuous time random walk in nonlinear Schrodinger equation with disorder

被引：6

作者：

Iomin, A. ^{[1
]}

机构：

[1] Technion, Dept Phys, IL-32000 Haifa, Israel

来源：

CHAOS SOLITONS & FRACTALS | 2016年 / 93卷

基金：

以色列科学基金会;

关键词：

Quantum nonlinear Schrodinger equation; Liouville equation; Quantum continuous time random walk; Quantum four-mode decay; Fractional Fokker-Planck equation; Subdiffusion; ANDERSON LOCALIZATION; ANOMALOUS DIFFUSION; TRANSPORT; DYNAMICS; DELOCALIZATION; CHAOS;

D O I：

10.1016/j.chaos.2016.09.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A quantum nonlinear Schrodinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied and subdiffusion of the wave packet is obtained with a transport exponent 1/2. It is shown that this transport exponent has pure quantum nature. A probabilistic description of subdiffusion in the framework of a quantum continuous time random walk is suggested and a quantum master equation is obtained. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：64 / 70

页数：7

共 43 条

[1] Visualization of exciton transport in ordered and disordered molecular solids [J].

Akselrod, Gleb M. ;

Deotare, Parag B. ;

Thompson, Nicholas J. ;

Lee, Jiye ;

Tisdale, William A. ;

Baldo, Marc A. ;

Menon, Vinod M. ;

Bulovic, Vladimir .

NATURE COMMUNICATIONS, 2014, 5

[2] ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES [J].

ANDERSON, PW .

PHYSICAL REVIEW, 1958, 109 (05) :1492-1505

[3]

[Anonymous], 1974, The fractional calculus theory and applications of differentiation and integration to arbitrary order, DOI DOI 10.1016/S0076-5392(09)60219-8

[4] Weak chaos in the disordered nonlinear Schrodinger chain: Destruction of Anderson localization by Arnold diffusion [J].

Basko, D. M. .

ANNALS OF PHYSICS, 2011, 326 (07) :1577-1655

[5]

Bateman H., 1955, Higher transcendental functions, California Institute of technology. Bateman Manuscript project

[6]

ben-Avraam D., 2000, DIFFUSION REACTIONS

[7] On the stability of a quantum dynamics of a Bose-Einstein condensate trapped in a one-dimensional toroidal geometry [J].

Berman, G. P. ;

Bishop, A. R. ;

Dalvit, D. A. R. ;

Shlyapnikov, G. V. ;

Tarkhanov, N. ;

Timmermans, E. M. .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2008, 47 (09) :2393-2408

[8] Quantum dynamics in the Fermi-Pasta-Ulam problem [J].

Berman, G. P. ;

Tarkhanov, N. .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2006, 45 (10) :1865-1887

[9]

Berman G.P., 1986, KIRENSKY I PHYS KRAS, DOI [10.13140/RG.2.2.12071.68001, DOI 10.13140/RG.2.2.12071.68001]

[10] METHOD OF QUASICLASSICAL APPROXIMATION FOR C-NUMBER PROJECTION IN COHERENT STATES BASIS [J].

BERMAN, GP ;

IOMIN, AM ;

ZASLAVSKY, GM .

PHYSICA D, 1981, 4 (01) :113-121

← 1 2 3 4 5 →