### Abstract

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function, where the Lindblad terms generally introduce a non-Hamiltonian flow. In addition to this, the Gaussian approximation yields dynamical equations for the covariances. The approximation becomes exact for linear Lindblad operators and a quadratic Hamiltonian. By viewing the Wigner function as a wave function on a coordinate space of doubled dimension, and the phase-space Lindblad equation as a Schrödinger equation with a non-Hermitian Hamiltonian, a further set of semiclassical equations are derived. These are capable of describing the interference terms in Wigner functions arising in superpositions of Gaussian states, as demonstrated for a cat state in an anharmonic oscillator subject to damping.

Original language | English |
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Article number | 365203 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 51 |

Issue number | 36 |

Early online date | 26 Jul 2018 |

DOIs | |

Publication status | Published - 7 Sep 2018 |

### Keywords

- Lindblad dynamics
- Quantum dynamics
- semiclassical methods
- wave packets

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## Student Theses

## Semiclassical methods for investigating open quantum systems and decoherence

Author: Plastow, T., 23 Jan 2020Supervisor: Schubert, R. C. V. (Supervisor)

Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)

## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*51*(36), [365203]. https://doi.org/10.1088/1751-8121/aad154