Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 51, Issue 36, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aad154
Keywords
quantum dynamics; semiclassical methods; Lindblad dynamics; wave packets
Categories
Funding
- Royal Society [UF130339]
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [758453]
- Engineering and Physical Sciences Research Council via the Doctoral Training Partnership [EP/M507878/1]
- European Research Council (ERC) [758453] Funding Source: European Research Council (ERC)
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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 Schrodinger equation with a non-Hermitian Hamiltonian, a further set of semiclassical equations are derived. These arc 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.
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