info:eu-repo/semantics/article
A Magnus approximation approach to harmonic systems with time-dependent frequencies
Fecha
2018-12Registro en:
Fosco, Cesar Daniel; Lombardo, Fernando Cesar; Mazzitelli, Francisco Diego; A Magnus approximation approach to harmonic systems with time-dependent frequencies; Academic Press Inc Elsevier Science; Annals of Physics (New York); 399; 12-2018; 258-269
0003-4916
CONICET Digital
CONICET
Autor
Fosco, Cesar Daniel
Lombardo, Fernando Cesar
Mazzitelli, Francisco Diego
Resumen
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.