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Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 140–168 (Mi aa1600)  
Research Papers

On some properties of the time evolution of quadratic open quantum systems

D. Robert

Département de Mathématiques, Laboratoire Jean Leray, CNRS-UMR 6629, Université de Nantes, 2 rue de la Houssinière, F-44322, Nantes Cedex 03, France
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Abstract: The paper is aimed at revisiting some mathematical properties that appear in open quantum systems with quadratic Hamiltonians. In particular, a discussion is included of some properties related to the notions of purity, separability, and entanglement, introduced by physicists in quantum information theory. The results are applied, among other things, to coupled harmonic oscillators appearing in the quantum Brownian motion. Moreover, the master equation is revisited, which was obtained for the time evolution of an open system coupled to an environment modeled by any quadratic Hamiltonians.
Keywords: quantum information theory, entanglement, master equation, Schrödinger equation, quantum Brownian motion.
Received: 11.12.2017
English version:
St. Petersburg Mathematical Journal, 2019, Volume 30, Issue 3, Pages 493–513
DOI: https://doi.org/10.1090/spmj/1556
Bibliographic databases:
Document Type: Article
Language: English
Citation: D. Robert, “On some properties of the time evolution of quadratic open quantum systems”, Algebra i Analiz, 30:3 (2018), 140–168; St. Petersburg Math. J., 30:3 (2019), 493–513
Citation in format AMSBIB
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