Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 28: Statistical Physics far from Equilibrium

DY 28.5: Talk

Thursday, March 17, 2011, 11:15–11:30, HÜL 186

Absence of Boltzmann-Gibbs equilibrium in an isolated quantum system with fixed energy and unrestricted participation of eigenstates. — •Boris Fine — Institute for Theoretical Physics, University of Heidelberg, 69120 Heidelberg, Germany

Usual approach to the foundations of quantum statistical physics is based on conventional micro-canonical ensemble as a starting point for deriving Boltzmann- Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical questions unanswered. Here we discuss these questions, thereby motivating the study of a natural alternative known as Quantum Micro-Canonical (QMC) ensemble. The QMC ensemble includes all possible superpositions of eigenstates of a large isolated quantum system provided all these superpositions have the same energy expectation value. We obtain analytically the statistics associated with the QMC ensemble for both the entire system and its small subsystem[1]. In a significant departure from the BG statistics, the average occupation numbers of quantum states exhibit in the present case weak algebraic dependence on energy. In the macroscopic limit, this dependence is routinely accompanied by the condensation into the lowest-energy quantum state. The above unconventional kind of equilibrium may be realizable after strong perturbations in small isolated quantum systems having large number of levels. We further suggest that the reason, why BG equilibrium commonly occurs in nature rather than the QMC-type equilibrium, has something to do with the notion of quantum collapse. [1] B.V. Fine, Phys. Rev. E v.80, p. 051130 (2009).