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

Authors:
Publisher website
Google Scholar
Abstract
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.
All Related Versions
Funding Information
  • National Science Foundation (NSF DMS 1201394)
  • Israel Science Foundation (ISF-1028)
  • United States-Israel Binational Science Foundation (BSF-2010132)

This publication has 18 references indexed in Scilit: