TL;DR
This paper explores quantum Kac's chaos, establishing its equivalence to 2-chaoticity and empirical measure convergence, and provides a new proof that chaos propagates under specific quantum Hamiltonian evolutions.
Contribution
It formalizes quantum Kac's chaos, proves its equivalence to key concepts, and offers a novel proof of chaos propagation in quantum mean field dynamics.
Findings
Quantum Kac's chaos is equivalent to 2-chaoticity and empirical measure convergence.
A new proof shows chaos propagates under certain quantum Hamiltonian evolutions.
The results extend classical chaos concepts to quantum many-body systems.
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.
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