Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

被引：2

作者：

Fishman, S. ^{[1
]}

Soffer, A. ^{[2
]}

机构：

[1] Technion, IL-32000 Haifa, Israel

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 07期

基金：

美国国家科学基金会; 以色列科学基金会;

关键词：

LANDAU-ZENER MODEL; ASYMPTOTIC COMPLETENESS; SYSTEMS;

D O I：

10.1063/1.4954498

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness. Published by AIP Publishing.

引用

页数：22