A Lindbladian From Feynman-Vernon
- URL: http://arxiv.org/abs/2312.16454v1
- Date: Wed, 27 Dec 2023 07:48:12 GMT
- Title: A Lindbladian From Feynman-Vernon
- Authors: Jose A. Magpantay
- Abstract summary: I derive a Lindbladian in a mechanical example, a point particle interacting with a bath of harmonic oscillators.
I also point out the causes of these terms, the Markov Lindbladian from the very local interaction of the point particle with the classical solutions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The effective dynamics of a system interacting with a bath or environment is
presented in two ways, (1) the (LGKS) replacement of the von Neuman equation
for the density matrix and (2) the Feynman-Vernon path-integral derivation, by
integrating out the bath degree of freedom, to arrive at a system's density
matrix. In this paper, I connect the two methods by deriving a Lindbladian in a
mechanical example, a point particle interacting with a bath of harmonic
oscillators, previously considered by Feynman and Vernon (FV) and expounded on
later by Caldeira and Leggett (CL). But the (FV)/(CL) results only in
non-Markov effect, memory terms from the bath interaction. To derive a
Lindbladian, I changed the interaction term they considered to take into
account the point particle interacting with the bath harmonic oscillators to
something more realistic. From the resulting path-integral expression of the
system's propagator for the density matrix, the Lindbladian and non-Markov
terms are read for this simple problem. I also point out the causes of these
terms, the Markov Lindbladian from the very local interaction of the point
particle with the classical solutions of the harmonic oscillator and the
non-Markov term from the global interaction of the point particle with the
fluctuation of the classical solutions.
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