Ayumu Sugita
Published 2006-02-27Version 1
We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what we observe can be written in a rather simple combination of local observables. Considering this limitation, we show that almost all states in a energy shell are practically indistinguishable from one another, and hence from the microcanonical ensemble. In particular, the expectation value of a macroscopic observable is very close to its microcanonical ensemble average for almost all states.
Comments: 6 pages, 1 figure, submitted to the Proceedings of the 6th International Summer School and Conference "Let's Face Chaos through Nonlinear Dynamics"
Journal: Nonlinear Phenomena in Complex Systems, Vol. 10, No. 2 (2007), pp. 192-195.
Time evolution of local observables after quenching to an integrable model
Uniform semiclassical approximation in quantum statistical mechanics
Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
