dorsal/arxiv
View SchemaFloquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
| Authors | Sigmund Kohler, Thomas Dittrich, Peter Hänggi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809088 |
| URL | https://arxiv.org/abs/quant-ph/9809088 |
| DOI | 10.1103/PhysRevE.55.300 |
| Journal | Phys.Rev. E55 (1997) 300-313 |
Abstract
Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the Wigner function. On all levels of approximation, these evolution equations retain the periodicity of the driving, so that their solutions have Floquet form and represent eigenfunctions of a non-unitary propagator over a single period of the driving. We discuss asymptotic states in the long-time limit as well as the conservative and the high-temperature limits. Numerical results obtained within the different Markov approximations are compared with the exact path-integral solution. The application of the improved Floquet-Markov scheme becomes increasingly important when considering stronger driving and lower temperatures.
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"abstract": "Using the parametrically driven harmonic oscillator as a working example, we\nstudy two different Markovian approaches to the quantum dynamics of a\nperiodically driven system with dissipation. In the simpler approach, the\ndriving enters the master equation for the reduced density operator only in the\nHamiltonian term. An improved master equation is achieved by treating the\nentire driven system within the Floquet formalism and coupling it to the\nreservoir as a whole. The different ensuing evolution equations are compared in\nvarious representations, particularly as Fokker-Planck equations for the Wigner\nfunction. On all levels of approximation, these evolution equations retain the\nperiodicity of the driving, so that their solutions have Floquet form and\nrepresent eigenfunctions of a non-unitary propagator over a single period of\nthe driving. We discuss asymptotic states in the long-time limit as well as the\nconservative and the high-temperature limits. Numerical results obtained within\nthe different Markov approximations are compared with the exact path-integral\nsolution. The application of the improved Floquet-Markov scheme becomes\nincreasingly important when considering stronger driving and lower\ntemperatures.",
"arxiv_id": "quant-ph/9809088",
"authors": [
"Sigmund Kohler",
"Thomas Dittrich",
"Peter H\u00e4nggi"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.55.300",
"journal_ref": "Phys.Rev. E55 (1997) 300-313",
"title": "Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator",
"url": "https://arxiv.org/abs/quant-ph/9809088"
},
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