期刊
PHYSICAL REVIEW LETTERS
卷 114, 期 6, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.114.060401
关键词
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资金
- U.S. National Science Foundation Grant [PHY-1019197]
- Office of Naval Research Grant [N00014-09-1-0502, N00014-12-1-0400]
- Institut Francilien de Recherche sur les Atomes Froids (IFRAF)
- Laboratoire de Physique des Lasers of Paris 13 University
- Division Of Physics
- Direct For Mathematical & Physical Scien [1402249] Funding Source: National Science Foundation
We show that for classical and quantum observables, the integrability-to-ergodicity transition leaves constant the sum of (a) the ensemble variance of the temporal average and (b) the ensemble average of temporal variance. The induced Frobenius (Hilbert-Schmidt) geometry of quantum observables encodes how eigenstate thermalization appears, the inverse participation ratio decreases, and the integrals of motion disappear during the transition. We use it to optimize the set of conserved quantities entering the generalized Gibbs ensemble for integrable, near-integrable, or mesoscopic systems.
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