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

DOI10.1063/1.4954498zbMath1348.81227arXiv1501.01290OpenAlexW3103953991MaRDI QIDQ3185694

Shmuel Fishman, Avy Soffer

Publication date: 4 August 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.01290

zbMATH Keywords

ergodic theoremtime-dependent Schrödinger equationadiabatic theoremmultiscale time averaging

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Ergodic theory of linear operators (47A35) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) (2)-body potential quantum scattering theory (81U05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (1)

Adiabatic theorems for general linear operators with time-independent domains

Cites Work

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• Adiabatic theorems and applications to the quantum Hall effect
• Completeness of wave operators in relativistic quantum mechanics
• The N-particle scattering problem: asymptotic completeness for short- range systems
• Asymptotic completeness for \(N\leq 4\) particle systems with the Coulomb-type interactions
• Minimal escape velocities
• Multiscale Time Averaging, Reloaded
• Elementary exponential error estimates for the adiabatic approximation.

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