# On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models

## Abstract

We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima-Zwanzig's projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove's limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.

- Authors:

- Department of Physics, Waseda University, Tokyo 169-8555 (Japan). E-mail: kazuya.yuasa@aist.go.jp
- Department of Applied Physics and Advanced Institute for Complex Systems, Waseda University, Tokyo 169-8555 (Japan)
- Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy)
- (Italy)
- Department of Physics, Waseda University, Tokyo 169-8555 (Japan)
- Dipartimento di Fisica, Universita di Bari, I-70126 Bari (Italy)

- Publication Date:

- OSTI Identifier:
- 20976738

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 3; Other Information: DOI: 10.1016/j.aop.2006.06.003; PII: S0003-4916(06)00134-5; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CORRELATIONS; EQUATIONS; FACTORIZATION; FORM FACTORS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; PARTICLE INTERACTIONS; QUANTUM MECHANICS

### Citation Formats

```
Yuasa, K., Tasaki, S., Facchi, P., Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Kimura, G., Nakazato, H., Ohba, I., Pascazio, S., and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari.
```*On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models*. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.06.003.

```
Yuasa, K., Tasaki, S., Facchi, P., Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Kimura, G., Nakazato, H., Ohba, I., Pascazio, S., & Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari.
```*On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models*. United States. doi:10.1016/j.aop.2006.06.003.

```
Yuasa, K., Tasaki, S., Facchi, P., Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Kimura, G., Nakazato, H., Ohba, I., Pascazio, S., and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari. Thu .
"On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models". United States.
doi:10.1016/j.aop.2006.06.003.
```

```
@article{osti_20976738,
```

title = {On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models},

author = {Yuasa, K. and Tasaki, S. and Facchi, P. and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari and Kimura, G. and Nakazato, H. and Ohba, I. and Pascazio, S. and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari},

abstractNote = {We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima-Zwanzig's projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove's limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.},

doi = {10.1016/j.aop.2006.06.003},

journal = {Annals of Physics (New York)},

number = 3,

volume = 322,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.