# On the application of Floquet theorem in development of time-dependent Lindbladians

## Abstract

In this paper, the mathematical framework providing a description of completely positive and trace preserving dynamics of open quantum systems is addressed. Special case of time-dependent Lindbladian governed by periodic Hamiltonian is concerned. It is proven that appropriate trace preserving dynamical map of such periodically driven system may be constructed by application of Floquet theory. Appropriate Lindbladian and Markovian master equation in weak coupling regime and resulting dynamical map are constructed. Some examples of application of developed technique are given.

- Authors:

- Institute of Theoretical Physics and Astrophysics, University of Gdansk, Wita Stwosza 57, 80-952 Gdansk (Poland)

- Publication Date:

- OSTI Identifier:
- 22306097

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 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; HAMILTONIANS; MARKOV PROCESS; MATHEMATICAL MODELS; PERIODICITY; QUANTUM MECHANICS; TIME DEPENDENCE

### Citation Formats

```
Szczygielski, Krzysztof, E-mail: fizksz@ug.edu.pl.
```*On the application of Floquet theorem in development of time-dependent Lindbladians*. United States: N. p., 2014.
Web. doi:10.1063/1.4891401.

```
Szczygielski, Krzysztof, E-mail: fizksz@ug.edu.pl.
```*On the application of Floquet theorem in development of time-dependent Lindbladians*. United States. doi:10.1063/1.4891401.

```
Szczygielski, Krzysztof, E-mail: fizksz@ug.edu.pl. Fri .
"On the application of Floquet theorem in development of time-dependent Lindbladians". United States.
doi:10.1063/1.4891401.
```

```
@article{osti_22306097,
```

title = {On the application of Floquet theorem in development of time-dependent Lindbladians},

author = {Szczygielski, Krzysztof, E-mail: fizksz@ug.edu.pl},

abstractNote = {In this paper, the mathematical framework providing a description of completely positive and trace preserving dynamics of open quantum systems is addressed. Special case of time-dependent Lindbladian governed by periodic Hamiltonian is concerned. It is proven that appropriate trace preserving dynamical map of such periodically driven system may be constructed by application of Floquet theory. Appropriate Lindbladian and Markovian master equation in weak coupling regime and resulting dynamical map are constructed. Some examples of application of developed technique are given.},

doi = {10.1063/1.4891401},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 55,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}

DOI: 10.1063/1.4891401

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