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Wigner distribution functions for complex dynamical systems: A path integral approach

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  • Sels, Dries
  • Brosens, Fons
  • Magnus, Wim
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    Abstract

    Starting from Feynman’s Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical phase space trajectory is found to contribute to the propagator. Inspired by Feynman’s and Vernon’s influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmonic oscillators. As an example we calculate the propagator for the reduced Wigner function associated with the Caldeira–Legett model.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112008412
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 392 (2013)
    Issue (Month): 2 ()
    Pages: 326-335

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    Handle: RePEc:eee:phsmap:v:392:y:2013:i:2:p:326-335

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Wigner distribution function; Reduced density matrix; Path integral; Propagator; Influence functionals;

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