# Eigenvalue problem of the Liouvillian of open quantum systems

## Abstract

It is argued that the Liouvillian that appears in the Liouville-von Neumann equation for open quantum systems can have complex eigenvalues. Attention is paid to the question whether the Liouvillian has an eigenvalue that are not given by the difference of the two Hamiltonian eigenvalues.

- Authors:

- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505 (Japan)
- Center for Complex Quantum Systems, Department of Physics, University of Texas at Austin, 2515 Speedway, Stop C1609, RLM 7.220, Austin, Texas 78712 (United States)

- Publication Date:

- OSTI Identifier:
- 22391057

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN-VLASOV EQUATION; EIGENVALUES; HAMILTONIANS; QUANTUM MECHANICS; QUANTUM SYSTEMS

### Citation Formats

```
Hatano, Naomichi, and Petrosky, Tomio.
```*Eigenvalue problem of the Liouvillian of open quantum systems*. United States: N. p., 2015.
Web. doi:10.1063/1.4912483.

```
Hatano, Naomichi, & Petrosky, Tomio.
```*Eigenvalue problem of the Liouvillian of open quantum systems*. United States. doi:10.1063/1.4912483.

```
Hatano, Naomichi, and Petrosky, Tomio. Tue .
"Eigenvalue problem of the Liouvillian of open quantum systems". United States.
doi:10.1063/1.4912483.
```

```
@article{osti_22391057,
```

title = {Eigenvalue problem of the Liouvillian of open quantum systems},

author = {Hatano, Naomichi and Petrosky, Tomio},

abstractNote = {It is argued that the Liouvillian that appears in the Liouville-von Neumann equation for open quantum systems can have complex eigenvalues. Attention is paid to the question whether the Liouvillian has an eigenvalue that are not given by the difference of the two Hamiltonian eigenvalues.},

doi = {10.1063/1.4912483},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1648,

place = {United States},

year = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4912483

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