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Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates
- Source :
- Physical Review E. 80
- Publication Year :
- 2009
- Publisher :
- American Physical Society (APS), 2009.
-
Abstract
- This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed, provided all these superpositions have the same fixed energy. Such a condition is not equivalent to the conventional micro-canonical condition, because the latter limits the participating eigenstates to a very narrow energy window. The statistics is obtained analytically for both the entire system and its small subsystem. In a significant departure from the Boltzmann-Gibbs 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. This work contains initial numerical tests of the above statistics for finite systems, and also reports the following numerical finding: When the basis states of large but finite random matrix Hamiltonians are expanded in terms of eigenstates, the participation of eigenstates in such an expansion obeys the newly obtained statistics. The above statistics might be observable in small quantum systems, but for the macroscopic systems, it rather reenforces doubts about self-sufficiency of non-relativistic quantum mechanics for justifying the Boltzmann-Gibbs equilibrium.<br />20 pages, 3 figures
- Subjects :
- Physics
Quantum Physics
Models, Statistical
Statistical Mechanics (cond-mat.stat-mech)
Quantum dynamics
FOS: Physical sciences
First quantization
Nonlinear Sciences - Chaotic Dynamics
Open quantum system
Energy Transfer
Models, Chemical
Quantum state
Quantum process
Quantum mechanics
Quantum Theory
Computer Simulation
Chaotic Dynamics (nlin.CD)
Quantum Physics (quant-ph)
Quantum statistical mechanics
Wave function collapse
Eigenstate thermalization hypothesis
Condensed Matter - Statistical Mechanics
Subjects
Details
- ISSN :
- 15502376 and 15393755
- Volume :
- 80
- Database :
- OpenAIRE
- Journal :
- Physical Review E
- Accession number :
- edsair.doi.dedup.....16f0d813716dcc8ad8dcabd9188556b5