Markovian evolution of Gaussian states in the semiclassical limit

We derive an approximate Gaussian solution of the Lindblad equation in the semiclassical limit, given a general Hamiltonian and linear coupling with the environment. The theory is carried out in the chord representation and describes the evolved quantum characteristic function, which gives direct ac...

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Bibliographic Details
Published inPhysics letters. A Vol. 374; no. 23; pp. 2315 - 2323
Main Authors Brodier, O., Ozorio de Almeida, A.M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 10.05.2010
Subjects
Approximation
Density
Evolution
Fourier transforms
Gaussian
Mathematical analysis
Representations
Wave propagation
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Summary:We derive an approximate Gaussian solution of the Lindblad equation in the semiclassical limit, given a general Hamiltonian and linear coupling with the environment. The theory is carried out in the chord representation and describes the evolved quantum characteristic function, which gives direct access to the Wigner function and the position representation of the density operator by Fourier transforms. The propagation is based on a system of non-linear equations taking place in a double phase space, which coincides with Heller's theory of unitary evolution of Gaussian wave packets when the Lindbladian part is zero. The example of a double well is worked out.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2010.03.059