Time evolution of closed macroscopic quantum systems towards thermal equilibrium

Abstract: Suppose we make a hot brick and a cold brick touch each other and isolate them from the rest of the world. Then, of course, energy will be transported from the hotter to the cooler until they reach the same temperature. This example illustrates the sense in which an isolated, macroscopic quantum system in a pure state will approach thermal equilibrium. Here, different macro-states correspond to mutually orthogonal subspaces of Hilbert space, each of very high dimension, thermal equilibrium to one of these subspaces, and entropy to the logarithm of the dimension. I will describe results concerning the unitary time evolution of such systems towards thermal equilibrium, the role played by a version of the eigenstate thermalization hypothesis, and some open questions.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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