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. © 2018 Elsevier Inc.
Registro:
Documento: |
Artículo
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Título: | A Magnus approximation approach to harmonic systems with time-dependent frequencies |
Autor: | Fosco, C.D.; Lombardo, F.C.; Mazzitelli, F.D. |
Filiación: | Instituto Balseiro and Centro Atómico Bariloche, Bariloche, R8402AGP, Argentina Departamento de Física Juan José Giambiagi, FCEyN UBA and IFIBA CONICET-UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
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Palabras clave: | Bogoliubov transformation; Effective action; Magnus approximation |
Año: | 2018
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Volumen: | 399
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Página de inicio: | 258
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Página de fin: | 269
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DOI: |
http://dx.doi.org/10.1016/j.aop.2018.10.016 |
Título revista: | Annals of Physics
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Título revista abreviado: | Ann. Phys.
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ISSN: | 00034916
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CODEN: | APNYA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00034916_v399_n_p258_Fosco |
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Citas:
---------- APA ----------
Fosco, C.D., Lombardo, F.C. & Mazzitelli, F.D.
(2018)
. A Magnus approximation approach to harmonic systems with time-dependent frequencies. Annals of Physics, 399, 258-269.
http://dx.doi.org/10.1016/j.aop.2018.10.016---------- CHICAGO ----------
Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D.
"A Magnus approximation approach to harmonic systems with time-dependent frequencies"
. Annals of Physics 399
(2018) : 258-269.
http://dx.doi.org/10.1016/j.aop.2018.10.016---------- MLA ----------
Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D.
"A Magnus approximation approach to harmonic systems with time-dependent frequencies"
. Annals of Physics, vol. 399, 2018, pp. 258-269.
http://dx.doi.org/10.1016/j.aop.2018.10.016---------- VANCOUVER ----------
Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D. A Magnus approximation approach to harmonic systems with time-dependent frequencies. Ann. Phys. 2018;399:258-269.
http://dx.doi.org/10.1016/j.aop.2018.10.016