Energy evolution in the time-dependent harmonic oscillator with arbitrary external forcing

DOI10.1016/S0034-4877(07)80099-1zbMath1134.81358arXivnlin/0606057OpenAlexW2041969981MaRDI QIDQ2472768

Andrei V. Kuzmin, Marko Robnik

Publication date: 25 February 2008

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0606057

zbMATH Keywords

linear oscillatorHamiltonian systemsclassical dynamicsenergy distribution functionWKB Approach

Mathematics Subject Classification ID

Hamilton's equations (70H05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Forced motions in linear vibration theory (70J35) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (1)

Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent

Cites Work

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• Adiabatic variation. I: Exponential property for the simple oscillator
• Adiabatic invariance to all orders
• Regular and chaotic dynamics.
• Adiabatic variation. II: Action change for the simple oscillator
• Adiabatic Invariant of the Harmonic Oscillator
• Exact analysis of adiabatic invariants in the time-dependent harmonic oscillator
• Energy Evolution in Time-Dependent Harmonic Oscillator
• Some properties of WKB series
• Exact energy distribution function in a time-dependent harmonic oscillator
• Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators
• The Adiabatic Invariant of the Linear or Nonlinear Oscillator
• Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly Periodic

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