Equilibration properties of small quantum systems: further examples
arXiv:1702.05909 · doi:10.1088/1751-8121/aa7f94
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 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 of the Hilbert space (no equilibration at all). Here we analyze several examples of simple systems where the behavior of can be investigated by analytical means. We first study the statistics of when the Hamiltonian governing the dynamics is random and drawn from a distribution invariant under the group U or O. We then investigate a quantum spin 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.
31 pages, 8 figures, 2 tables
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