A solvable model of the breakdown of the adiabatic approximation

DOI10.1063/5.0001813zbMath1459.81037arXiv2001.07085OpenAlexW3001120365MaRDI QIDQ5141041

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Publication date: 17 December 2020

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

Full work available at URL: https://arxiv.org/abs/2001.07085

zbMATH Keywords

time-dependent family of \(1D\) Schrödinger equations

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Time-dependent Schrödinger equations and Dirac equations (35Q41) Special quantum systems, such as solvable systems (81Q80)

Uses Software

• DLMF

Cites Work

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• Dynamical crossing of an infinitely degenerate critical point
• On adiabatic pair creation
• The surfboard Schrödinger equations
• Remarks on convergence of the Feynman path integrals
• Adiabatic perturbation theory in quantum dynamics
• Non-stochasticity of time-dependent quadratic Hamiltonians and the spectra of canonical transformations
• On the adiabatic theorem when eigenvalues dive into the continuum

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