cea-01484658
https://cea.hal.science/cea-01484658
https://cea.hal.science/cea-01484658/document
https://cea.hal.science/cea-01484658/file/1702.05909.pdf
arxiv:1702.05909
[CEA] CEA - Commissariat à l'énergie atomique
[CNRS] CNRS - Centre national de la recherche scientifique
[DSM-IPHT] IPHT
[CEA-UPSAY] CEA - Université Paris-Saclay
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[CEA-UPSAY-SACLAY] CEA-UPSAY-SACLAY
[CEA-DRF] Direction de Recherche Fondamentale
[TEST-HALCNRS] Collection test HAL CNRS
[GS-MATHEMATIQUES] Graduate School Mathématiques
[GS-PHYSIQUE] Graduate School Physique
Equilibration properties of small quantum systems: further examples
Luck, J. M.
[PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
UNDEFINED
It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace $T$ of this matrix measures the degree of equilibration of the system prepared in a typical state of the preferential basis. This quantity may vary between unity (ideal equilibration) and the dimension $N$ of the Hilbert space (no equilibration at all). Here we analyze several examples of simple systems where the behavior of $T$ can be investigated by analytical means. We first study the statistics of $T$ when the Hamiltonian governing the dynamics is random and drawn from a distribution invariant under the group U$(N)$ or O$(N)$. We then investigate a quantum spin $S$ in a tilted magnetic field making an arbitrary angle with the preferred quantization axis, as well as a tight-binding particle on a finite electrified chain. The last two cases provide examples of the interesting situation where varying a system parameter -- such as the tilt angle or the electric field -- through some scaling regime induces a continuous transition from good to bad equilibration properties.
2017-03-07
2017-03-07
en