dorsal/arxiv
View SchemaReduced density matrices of oscillator systems
| Authors | V. V. Dodonov, O. V. Man'ko, V. I. Man'ko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210030 |
| URL | https://arxiv.org/abs/quant-ph/0210030 |
| Journal | Journal of Russian Laser Research, vol. 16, no. 1, p. 1--56 (1995) |
Abstract
We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a possibility of using the Fokker-Planck equation to describe this evolution. Studying different interaction Hamiltonians, we show that unambiguous reduction to the Fokker-Planck equation is possible only within the framework of the so called rotating-wave approximation. As special cases we consider in detail the evolution of two coupled oscillators and relaxation of a charged oscillator in a uniform magnetic field.
{
"annotation_id": "53484622-b221-4cf1-9cce-cfba353ba761",
"date_created": "2026-03-02T18:01:53.167000Z",
"date_modified": "2026-03-02T18:01:53.167000Z",
"file_hash": "85b5ac419d17e763b57190ba62ffd7e359b1ca78c67c7cd7ebe4d5d3a9124637",
"private": false,
"record": {
"abstract": "We study the evolution of an oscillator interacting via the most general\nbilinear coupling (with time-independent coefficients) with an ``environment\u0027\u0027\nconsisting of a set of other harmonic oscillators. We are mainly interested in\na possibility of using the Fokker-Planck equation to describe this evolution.\nStudying different interaction Hamiltonians, we show that unambiguous reduction\nto the Fokker-Planck equation is possible only within the framework of the so\ncalled rotating-wave approximation. As special cases we consider in detail the\nevolution of two coupled oscillators and relaxation of a charged oscillator in\na uniform magnetic field.",
"arxiv_id": "quant-ph/0210030",
"authors": [
"V. V. Dodonov",
"O. V. Man\u0027ko",
"V. I. Man\u0027ko"
],
"categories": [
"quant-ph"
],
"journal_ref": "Journal of Russian Laser Research, vol. 16, no. 1, p. 1--56 (1995)",
"title": "Reduced density matrices of oscillator systems",
"url": "https://arxiv.org/abs/quant-ph/0210030"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "6de890ef-d830-4d45-8c1a-fad02c17366b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}