Equilibration properties of small quantum systems: further examples. (4th August 2017)

• Record Type: Journal Article
• Authors: Luck, J M
• Is Part Of: Journal of physics. Volume 50:Number 35(2017)
• Publication Date: 2017-08-04
• Subjects: equilibration -- closed quantum systems -- localization -- thermalization; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa7f94
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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 crossover from good to bad equilibration properties.