Eigenfunctions and quantum transport with applications to trimmed Schrödinger operators

被引:0
|
作者
Hislop, Peter D. [1 ]
Kirsch, Werner [2 ]
Krishna, M. [3 ]
机构
[1] Univ Kentucky, Dept Biol, Lexington, KY 40506 USA
[2] Fernuniv, Fak Math & Informat, D-58097 Hagen, Germany
[3] Ashoka Univ, Plot 2, Sonepat 131029, Haryana, India
关键词
SCHRODINGER-OPERATORS; ANDERSON MODEL; LOCALIZATION; SPECTRUM; DYNAMICS; DISORDER; DELOCALIZATION; SUBORDINACY;
D O I
10.1063/5.0192715
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We provide a simple proof of dynamical delocalization, that is, time-increasing lower bounds on quantum transport for discrete, one-particle Schr & ouml;dinger operators on & ell;(2)(Z(d)), provided solutions to the Schr & ouml;dinger equation satisfy certain growth conditions. The proof is based on basic resolvent identities and the Combes-Thomas estimate on the exponential decay of the Green's function. As a consequence, we prove that generalized eigenfunctions for energies outside the spectrum of H must grow exponentially in some directions. We also prove that if H has any absolutely continuous spectrum, then the Schr & ouml;dinger operator exhibits dynamical delocalization. We apply the general result to Gamma-trimmed Schr & ouml;dinger operators, with periodic Gamma, and prove dynamical delocalization for these operators. These results also apply to the Gamma-trimmed Anderson model, providing a random, ergodic model exhibiting both dynamical localization in an energy interval and dynamical delocalization.
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页数:16
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