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arXiv · 1807.06755

A Magnus approximation approach to harmonic systems with time-dependent frequencies

C. D. Fosco·F. C. Lombardo·F. D. Mazzitelli
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Abstract

We use a Magnus approximation at the level of the equations of motion for a harmonic system with a time-dependent frequency, to find an expansion for its in-out effective action, and a unitary expansion for the Bogoliubov transformation between in and out states. The dissipative effects derived therefrom are compared with the ones obtained from perturbation theory in powers of the time-dependent piece in the frequency, and with those derived using multiple scale analysis in systems with parametric resonance. We also apply the Magnus expansion to the in-in effective action, to construct reality and causal equations of motion for the external system. We show that the nonlocal equations of motion can be written in terms of a "retarded Fourier transform" evaluated at the resonant frequency.

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C. D. Fosco, F. C. Lombardo, F. D. Mazzitelli. 2018-07-18. A Magnus approximation approach to harmonic systems with time-dependent frequencies. https://doi.org/10.1016/j.aop.2018.10.016

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