Communications in Mathematical Sciences

Volume 16 (2018)

Number 7

Quantum Kac’s chaos

Pages: 1801 – 1825



George Androulakis (Department of Mathematics, University of South Carolina, Columbia, S.C., U.S.A.)

Rade Musulin (Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Fl., U.S.A.)


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.


Kac’s chaos, quantum Kac’s chaos, empirical measure, Hartree equation

2010 Mathematics Subject Classification

35Q83, 37K99, 81Q50

Received 1 December 2017

Accepted 12 June 2018

Published 7 March 2019