dorsal/arxiv
View SchemaOn convergence to equilibrium in strongly coupled Bogoliubov's oscillator model
| Authors | V. Strokov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612202 |
| URL | https://arxiv.org/abs/quant-ph/0612202 |
| Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2007, Vol. 10, No. 4, pp. 573-589 |
Abstract
We examine classical Bogoliubov's model of a particle coupled to a heat bath which consists of infinitely many stochastic oscillators. Bogoliubov's result suggests that, in the stochastic limit, the model exhibits convergence to thermodynamical equilibrium. It has recently been shown that the system does attain the equilibrium if the coupling constant is small enough. We show that in the case of the large coupling constant the distribution function $\rho_{S}(q,p,t)\to 0$ pointwise as $t\to\infty$. This implies that if there is convergence to equilibrium, then the limit measure has no finite momenta. Besides, the probability to find the particle in any finite domain of phase space tends to zero. This is also true for domains in the coordinate space and in the momentum space.
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"abstract": "We examine classical Bogoliubov\u0027s model of a particle coupled to a heat bath\nwhich consists of infinitely many stochastic oscillators. Bogoliubov\u0027s result\nsuggests that, in the stochastic limit, the model exhibits convergence to\nthermodynamical equilibrium. It has recently been shown that the system does\nattain the equilibrium if the coupling constant is small enough. We show that\nin the case of the large coupling constant the distribution function\n$\\rho_{S}(q,p,t)\\to 0$ pointwise as $t\\to\\infty$. This implies that if there is\nconvergence to equilibrium, then the limit measure has no finite momenta.\nBesides, the probability to find the particle in any finite domain of phase\nspace tends to zero. This is also true for domains in the coordinate space and\nin the momentum space.",
"arxiv_id": "quant-ph/0612202",
"authors": [
"V. Strokov"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"journal_ref": "Infinite Dimensional Analysis, Quantum Probability and Related\n Topics, 2007, Vol. 10, No. 4, pp. 573-589",
"title": "On convergence to equilibrium in strongly coupled Bogoliubov\u0027s oscillator model",
"url": "https://arxiv.org/abs/quant-ph/0612202"
},
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