# Non-Markovian quantum Brownian motion of a harmonic oscillator

## Abstract

We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab., IL (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 10118416

- Report Number(s):
- ANL/CHM/PP-79434

ON: DE94005922

- DOE Contract Number:
- W-31109-ENG-38

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: [1994]

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BROWNIAN MOVEMENT; HARMONIC OSCILLATORS; QUANTUM MECHANICS; MARKOV PROCESS; EQUATIONS; 661100; 665400; CLASSICAL AND QUANTUM MECHANICS; QUANTUM PHYSICS ASPECTS OF CONDENSED MATTER

### Citation Formats

```
Tang, J.
```*Non-Markovian quantum Brownian motion of a harmonic oscillator*. United States: N. p., 1994.
Web. doi:10.2172/10118416.

```
Tang, J.
```*Non-Markovian quantum Brownian motion of a harmonic oscillator*. United States. https://doi.org/10.2172/10118416

```
Tang, J. Tue .
"Non-Markovian quantum Brownian motion of a harmonic oscillator". United States. https://doi.org/10.2172/10118416. https://www.osti.gov/servlets/purl/10118416.
```

```
@article{osti_10118416,
```

title = {Non-Markovian quantum Brownian motion of a harmonic oscillator},

author = {Tang, J},

abstractNote = {We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.},

doi = {10.2172/10118416},

url = {https://www.osti.gov/biblio/10118416},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1994},

month = {2}

}

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