On the Emergence of the Microcanonical Description from a Pure State

Details On the Emergence of the Microcanonical Description from a Pure State On the Emergence of the Microcanonical Description from a Pure State

2001-12-24

arxiv.org/abs/cond-mat/0112439v2

Int.J.Mod.Phys. A18 (2003) 2947-2994

Physics

Condensed Matter

Statistical Mechanics

58 pages, 2 figures. A reference added

Scientific paper

10.1142/S0217751X03015143

We study, in general terms, the process by which a pure state can ``self-thermalize'' and {\em appear} to be described by a microcanonical density matrix. This requires a quantum mechanical version of the Gibbsian coarse graining that conceptually underlies classical statistical mechanics. We introduce some extra degrees of freedom that are necessary for this. Interaction between these degrees and the system can be understood as a process of resonant absorption and emission of ``soft quanta''. This intuitive picture allows one to state a criterion for when self thermalization occurs. This paradigm also provides a method for calculating the thermalization rate using the usual formalism of atomic physics for calculating decay rates. We contrast our prescription for coarse graining, which is somewhat dynamical, with the earlier approaches that are intrinsically kinematical. An important motivation for this study is the black hole information paradox.

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