dorsal/arxiv
View SchemaStochastic description for open quantum systems
| Authors | Esteban Calzetta, Albert Roura, Enric Verdaguer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011097 |
| URL | https://arxiv.org/abs/quant-ph/0011097 |
| DOI | 10.1016/S0378-4371(02)01521-2 |
| Journal | Physica A319 (2003) 188-212 |
Abstract
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a Gaussian state. Using the influence functional formalism a formal Langevin equation can be introduced to describe the system's fully quantum properties even beyond the semiclassical regime. It is shown that the reduced Wigner function for the system is exactly the formal distribution function resulting from averaging both over the initial conditions and the stochastic source of the formal Langevin equation. The master equation for the reduced density matrix is then obtained in the same way a Fokker-Planck equation can always be derived from a Langevin equation characterizing a stochastic process. We also show that a subclass of quantum correlation functions for the system can be deduced within the stochastic description provided by the Langevin equation. It is emphasized that when the system is not Markovian more information can be extracted from the Langevin equation than from the master equation.
{
"annotation_id": "084f9c78-086b-4579-9d09-2c2ab61a9b6c",
"date_created": "2026-03-02T18:01:42.539000Z",
"date_modified": "2026-03-02T18:01:42.539000Z",
"file_hash": "a5e7f5d154097abf23f31c40d40c6c9c9105ceb507feb7d1d55bad83cea5fa44",
"private": false,
"record": {
"abstract": "A linear open quantum system consisting of a harmonic oscillator linearly\ncoupled to an infinite set of independent harmonic oscillators is considered;\nthese oscillators have a general spectral density function and are initially in\na Gaussian state. Using the influence functional formalism a formal Langevin\nequation can be introduced to describe the system\u0027s fully quantum properties\neven beyond the semiclassical regime. It is shown that the reduced Wigner\nfunction for the system is exactly the formal distribution function resulting\nfrom averaging both over the initial conditions and the stochastic source of\nthe formal Langevin equation. The master equation for the reduced density\nmatrix is then obtained in the same way a Fokker-Planck equation can always be\nderived from a Langevin equation characterizing a stochastic process. We also\nshow that a subclass of quantum correlation functions for the system can be\ndeduced within the stochastic description provided by the Langevin equation. It\nis emphasized that when the system is not Markovian more information can be\nextracted from the Langevin equation than from the master equation.",
"arxiv_id": "quant-ph/0011097",
"authors": [
"Esteban Calzetta",
"Albert Roura",
"Enric Verdaguer"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"gr-qc",
"hep-ph"
],
"doi": "10.1016/S0378-4371(02)01521-2",
"journal_ref": "Physica A319 (2003) 188-212",
"title": "Stochastic description for open quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0011097"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c03ab94f-1af8-49f4-9650-68ba791810c4",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}