HAL CCSD
Equilibration properties of small quantum systems: further examples
Luck, J. M.
Institut de Physique Théorique - UMR CNRS 3681 (IPHT) ; Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
30 pages, 8 figures, 3 tables
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
https://cea.hal.science/cea-01484658
2017
ARXIV: 1702.05909
info:eu-repo/semantics/altIdentifier/arxiv/1702.05909
en
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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
info:eu-repo/semantics/OpenAccess