Quantum Kac's Chaos
arXiv:1711.09997 · doi:10.4310/cms.2018.v16.n7.a3
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.
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