Demystifying the constancy of the Ermakov–Lewis invariant for a time-dependent oscillator

DOI10.1142/S0217732318300057zbMath1383.34055arXiv1712.07328OpenAlexW2780478443MaRDI QIDQ4608734

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Publication date: 23 March 2018

Published in: Modern Physics Letters A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.07328

zbMATH Keywords

Ermakov-Lewis invariantSchwinger effecttime-dependent harmonic oscillatorBogoliubov coefficients

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Quantum field theory; related classical field theories (81T99)

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Inverting a normal harmonic oscillator: physical interpretation and applications ⋮ Comment on demystifying the constancy of the Ermakov–Lewis invariant for a time-dependent oscillator ⋮ Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling ⋮ Quantum uncertainty as an intrinsic clock ⋮ Symmetries and conservation laws for the generalized n‐dimensional Ermakov system ⋮ An integral of motion for the damped cubic-quintic Duffing oscillator with variable coefficients ⋮ A note on generalization of the Ermakov–Lewis invariant and its demystification ⋮ Nonlocal transformations of the generalized Liénard type equations and dissipative Ermakov-Milne-Pinney systems

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