# Non-Markovian generalization of the Lindblad theory of open quantum systems

## Abstract

A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.

- Authors:

- Physikalisches Institut, Universitaet Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg (Germany)

- Publication Date:

- OSTI Identifier:
- 20982062

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022103; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; INFORMATION THEORY; MARKOV PROCESS; PROJECTION OPERATORS; QUANTUM INFORMATION; QUANTUM MECHANICS; STATISTICAL MECHANICS; SUPEROPERATORS

### Citation Formats

```
Breuer, Heinz-Peter.
```*Non-Markovian generalization of the Lindblad theory of open quantum systems*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022103.

```
Breuer, Heinz-Peter.
```*Non-Markovian generalization of the Lindblad theory of open quantum systems*. United States. doi:10.1103/PHYSREVA.75.022103.

```
Breuer, Heinz-Peter. Thu .
"Non-Markovian generalization of the Lindblad theory of open quantum systems". United States.
doi:10.1103/PHYSREVA.75.022103.
```

```
@article{osti_20982062,
```

title = {Non-Markovian generalization of the Lindblad theory of open quantum systems},

author = {Breuer, Heinz-Peter},

abstractNote = {A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and from the theory of positive maps, we derive a class of correlated projection superoperators that take into account in an efficient way statistical correlations between the open system and its environment. The result is used to develop a generalization of the Lindblad theory to the regime of highly non-Markovian quantum processes in structured environments.},

doi = {10.1103/PHYSREVA.75.022103},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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