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 phasespace dynamics is obtained for the centre of a Gaussian Wigner function, where the Lindblad terms generally introduce a nonHamiltonian 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 phasespace Lindblad equation as a Schrödinger equation with a nonHermitian 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 

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)
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