dorsal/arxiv
View SchemaQuantum Dynamical Effects as a Singular Perturbation for Observables in Open Quasi-Classical Nonlinear Mesoscopic Systems
| Authors | Gennady P. Berman, Fausto Borgonovi, Diego A. R. Dalvit |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604024 |
| URL | https://arxiv.org/abs/quant-ph/0604024 |
Abstract
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular "quantum" perturbation for observables in some "mesoscopic" region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose-Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.
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"abstract": "We review our results on a mathematical dynamical theory for observables for\nopen many-body quantum nonlinear bosonic systems for a very general class of\nHamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian\nprovide a singular \"quantum\" perturbation for observables in some \"mesoscopic\"\nregion of parameters. In particular, quantum effects result in secular terms in\nthe dynamical evolution, that grow in time. We argue that even for open quantum\nnonlinear systems in the deep quasi-classical region, these quantum effects can\nsurvive after decoherence and relaxation processes take place. We demonstrate\nthat these quantum effects in open quantum systems can be observed, for\nexample, in the frequency Fourier spectrum of the dynamical observables, or in\nthe corresponding spectral density of noise. Estimates are presented for\nBose-Einstein condensates, low temperature mechanical resonators, and nonlinear\noptical systems prepared in large amplitude coherent states. In particular, we\nshow that for Bose-Einstein condensate systems the characteristic time of\ndeviation of quantum dynamics for observables from the corresponding classical\ndynamics coincides with the characteristic time-scale of the well-known quantum\nnonlinear effect of phase diffusion.",
"arxiv_id": "quant-ph/0604024",
"authors": [
"Gennady P. Berman",
"Fausto Borgonovi",
"Diego A. R. Dalvit"
],
"categories": [
"quant-ph"
],
"title": "Quantum Dynamical Effects as a Singular Perturbation for Observables in Open Quasi-Classical Nonlinear Mesoscopic Systems",
"url": "https://arxiv.org/abs/quant-ph/0604024"
},
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