# Quantum dynamical semigroups for finite and infinite Bose systems

## Abstract

A new class of quasifree quantum Markov semigroups on C*-algebras of canonical commutation relations is introduced and discussed. Two applications to decoherence in the Heisenberg representation are given. In the first one the dynamical semigroup which leads to the appearance of decoherence induced superselection rules corresponding to the boundary conditions of a quantum particle in a finite interval is considered. The second example analyzes the possibility of the transition from infinite systems to systems with a finite number of degrees of freedom.

- Authors:

- Physics Faculty, University of Bielefeld, Universitaetstrasse 25, 33615 Bielefeld (Germany) and BiBoS, University of Bielefeld, Universitaetstrasse 25, 33615 Bielefeld (Germany)
- (Poland)

- Publication Date:

- OSTI Identifier:
- 20929609

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 1; Other Information: DOI: 10.1063/1.2406053; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; BOUNDARY CONDITIONS; COMMUTATION RELATIONS; DEGREES OF FREEDOM; GROUP THEORY; HEISENBERG PICTURE; MARKOV PROCESS; QUANTUM DECOHERENCE; QUANTUM MECHANICS; SUPERSELECTION RULES

### Citation Formats

```
Blanchard, Ph., Hellmich, M., Lugiewicz, P., Olkiewicz, R., and Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50204 Wroclaw.
```*Quantum dynamical semigroups for finite and infinite Bose systems*. United States: N. p., 2007.
Web. doi:10.1063/1.2406053.

```
Blanchard, Ph., Hellmich, M., Lugiewicz, P., Olkiewicz, R., & Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50204 Wroclaw.
```*Quantum dynamical semigroups for finite and infinite Bose systems*. United States. doi:10.1063/1.2406053.

```
Blanchard, Ph., Hellmich, M., Lugiewicz, P., Olkiewicz, R., and Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50204 Wroclaw. Mon .
"Quantum dynamical semigroups for finite and infinite Bose systems". United States.
doi:10.1063/1.2406053.
```

```
@article{osti_20929609,
```

title = {Quantum dynamical semigroups for finite and infinite Bose systems},

author = {Blanchard, Ph. and Hellmich, M. and Lugiewicz, P. and Olkiewicz, R. and Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50204 Wroclaw},

abstractNote = {A new class of quasifree quantum Markov semigroups on C*-algebras of canonical commutation relations is introduced and discussed. Two applications to decoherence in the Heisenberg representation are given. In the first one the dynamical semigroup which leads to the appearance of decoherence induced superselection rules corresponding to the boundary conditions of a quantum particle in a finite interval is considered. The second example analyzes the possibility of the transition from infinite systems to systems with a finite number of degrees of freedom.},

doi = {10.1063/1.2406053},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 48,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}

DOI: 10.1063/1.2406053

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