A Nonlinear Adiabatic Theorem for Coherent States

DOI10.1007/978-3-0348-0466-0_5zbMath1281.35076OpenAlexW4213011137MaRDI QIDQ4912945

Rémi Carles, Clotilde Fermanian-Kammerer

Publication date: 2 April 2013

Published in: Microlocal Methods in Mathematical Physics and Global Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0466-0_5

zbMATH Keywords

coherent statesadiabatic theorem1-d cubic nonlinear Schrödinger equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Cites Work

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• Nonlinear Schrödinger equation with time dependent potential
• Nonlinear coherent states and Ehrenfest time for Schrödinger equation
• Adiabatic perturbation theory in quantum dynamics
• A nonlinear adiabatic theorem for coherent states
• Twisted pseudodifferential calculus and application to the quantum evolution of molecules
• Molecular propagation through electron energy level crossings
• Exponentially accurate semiclassical dynamics: Propagation, localization, Ehrenfest times, scattering, and more general states.
• Adiabatic decoupling and time-dependent Born-Oppenheimer theory

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