Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit
File(s)
Accepted version
Author(s)
Graefe, EM
Longstaff, B
Plastow, T
Schubert, R
Type
Journal Article
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.
Date Issued
2018-09-07
Date Acceptance
2018-07-05
Citation
Journal of Physics A: Mathematical and Theoretical, 2018, 51 (36)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
51
Issue
36
Copyright Statement
© 2018 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at https://dx.doi.org/10.1088/1751-8121/aad154
Sponsor
The Royal Society
Commission of the European Communities
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000440044400001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
UF130339
758453
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Mathematical
Physics
quantum dynamics
semiclassical methods
Lindblad dynamics
wave packets
GENERAL FORMALISM
HYBRID MECHANICS
QUANTUM-SYSTEMS
COMPLEX FLUIDS
THERMODYNAMICS
EVOLUTION
Publication Status
Published
Article Number
365203
Date Publish Online
2018-07-26