Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit

E M Graefe, B Longstaff, T Plastow, R Schubert

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)
314 Downloads (Pure)


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 languageEnglish
Article number365203
Number of pages20
JournalJournal of Physics A: Mathematical and Theoretical
Issue number36
Early online date26 Jul 2018
Publication statusPublished - 7 Sept 2018


  • Lindblad dynamics
  • Quantum dynamics
  • semiclassical methods
  • wave packets


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