On the definition of (and approach to) thermal equilibrium in an isolated macroscopic system:quantum and classical

by Joel Lebowitz (Dipartimenti di Fisica e di Matematica, Rutgers University)

Tuesday 24 May 2016, 16:00 → 17:00 Europe/Rome

Dip. di Fisic

This seminar  will discuss the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may however not be in microscopic thermal equilibrium (MITE). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. 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. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but MITE fails to hold for any phase point. The approach to equilibrium from an initial nonequilibrium state will also be discussed.