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Mathematical Physics Seminar

Macroscopic and Microscopic Thermal Equilibrium

Roderich Tumulka - Eberhard-Karls University of Tuebingen

Location:  HILL 525
Date & time: Friday, 25 August 2017 at 12:00PM - 3:00PM


This talk is about the notion of thermal equilibrium, and of approach to thermal equilibrium, for an individual closed macroscopic quantum system. Of such a system we say that it is in macroscopic thermalequilibrium (MATE) if it is in a state in which all macroscopic observables assume rather sharply the equilibrium values obtained from thermodynamics.  A stronger requirement than MATE is that evenmicroscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical,  ensemble for the whole system.  Of such a system we say that it is in microscopic thermal equilibrium (MITE). The distinction between MITE and MATE is particularly relevant for systems with many-body  localization (MBL) for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE.  However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions psi) in an energy shell, then for generic macroscopic systems, including those with MBL, most psi are in both MATE and MITE.  We explore and compare the two notions of equilibrium. 

This is  joint work with Sheldon Goldstein, David Huse, and Joel Lebowitz.


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