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.
|Number of pages||20|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Early online date||26 Jul 2018|
|Publication status||Published - 7 Sept 2018|
- Lindblad dynamics
- Quantum dynamics
- semiclassical methods
- wave packets
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23 Jan 2020
Supervisor: Schubert, R. C. V. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)File