Axiomatic construction of quantum Langevin equations
Statistical Mechanics
2019-05-21 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem is presented. The case of a single harmonic oscillator coupled to a large external bath is analysed in detail. This allows to distinguish a markovian semi-classical approach, due to Bedeaux and Mazur, from a non-markovian full quantum approach, due to to Ford, Kac and Mazur. The quantum-fluctuation-dissipation theorem is seen to be incompatible with a markovian dynamics. Possible applications to the quantum spherical model are discussed.
Cite
@article{arxiv.1809.08975,
title = {Axiomatic construction of quantum Langevin equations},
author = {Rúbia Araújo and Sascha Wald and Malte Henkel},
journal= {arXiv preprint arXiv:1809.08975},
year = {2019}
}
Comments
1 + 33 pages, 4 figures. Major revision. J. Stat. Mech at press