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

Dries Sels, Fons Brosens and Wim Magnus

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 2, 326-335

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.

Keywords: Wigner distribution function; Reduced density matrix; Path integral; Propagator; Influence functionals (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:2:p:326-335

DOI: 10.1016/j.physa.2012.09.007

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