dorsal/arxiv
View SchemaOn the averaged quantum dynamics by white-noise Hamiltonians with and without dissipation
| Authors | Werner Fischer, Hajo Leschke, Peter Mueller |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9807065 |
| URL | https://arxiv.org/abs/quant-ph/9807065 |
| DOI | 10.1002/andp.2090070203 |
| Journal | Annalen Phys. 7 (1998) 59-100 |
Abstract
Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic, time-independent and quadratic, the Weyl-Wigner symbol of the other part is a homogeneous Gaussian random field which is delta correlated in time, but smoothly correlated in position and momentum. The averaged dynamics of the resulting white-noise system is shown to be a monotone mixing increasing quantum-dynamical semigroup. Its generator is computed explicitly. Typically, in the course of time the mean energy of such a system grows linearly to infinity. In the second part of the paper an extended model is studied, which, in addition, accounts for dissipation by coupling the white-noise system linearly to a quantum-mechanical harmonic heat bath. It is demonstrated that, under suitable assumptions on the spectral density of the heat bath, the mean energy then saturates for long times.
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"abstract": "Exact results are derived on the averaged dynamics of a class of random\nquantum-dynamical systems in continuous space. Each member of the class is\ncharacterized by a Hamiltonian which is the sum of two parts. While one part is\ndeterministic, time-independent and quadratic, the Weyl-Wigner symbol of the\nother part is a homogeneous Gaussian random field which is delta correlated in\ntime, but smoothly correlated in position and momentum. The averaged dynamics\nof the resulting white-noise system is shown to be a monotone mixing increasing\nquantum-dynamical semigroup. Its generator is computed explicitly. Typically,\nin the course of time the mean energy of such a system grows linearly to\ninfinity. In the second part of the paper an extended model is studied, which,\nin addition, accounts for dissipation by coupling the white-noise system\nlinearly to a quantum-mechanical harmonic heat bath. It is demonstrated that,\nunder suitable assumptions on the spectral density of the heat bath, the mean\nenergy then saturates for long times.",
"arxiv_id": "quant-ph/9807065",
"authors": [
"Werner Fischer",
"Hajo Leschke",
"Peter Mueller"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1002/andp.2090070203",
"journal_ref": "Annalen Phys. 7 (1998) 59-100",
"title": "On the averaged quantum dynamics by white-noise Hamiltonians with and without dissipation",
"url": "https://arxiv.org/abs/quant-ph/9807065"
},
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