Quantum Kac's Chaos
Mathematical Physics
2019-05-14 v2 Dynamical Systems
math.MP
Abstract
We study the notion of quantum Kac's chaos which was implicitly introduced by Spohn and explicitly formulated by Gottlieb. We prove the analogue of a result of Sznitman which gives the equivalence of Kac's chaos to 2-chaoticity and to convergence of empirical measures. Finally we give a simple, different proof of a result of Spohn which states that chaos propagates with respect to certain Hamiltonians that define the evolution of the mean field limit for interacting quantum systems.
Keywords
Cite
@article{arxiv.1711.09997,
title = {Quantum Kac's Chaos},
author = {George Androulakis and Rade Musulin},
journal= {arXiv preprint arXiv:1711.09997},
year = {2019}
}
Comments
The original arXiv submission is replaced in order to better reflect the content in the printed version in: Commun. Math. Sci. Vol. 16, No 7, (2018), 1801-1825