Continuous phase-space methods on discrete phase spaces
Departmento de Física, Universidad de Chile - Santiago, Chile and Scuola Internazionale Superiore di Studi Avanzati - Trieste, Italy
Received: 17 August 2015
Accepted: 25 September 2015
We show that discrete quasiprobability distributions defined via the discrete Heisenberg-Weyl group can be obtained as discretizations of the continuous SU(N) quasiprobability distributions. This is done by identifying the phase-point operators with the continuous quantisation kernels evaluated at special points of the phase space. As an application we discuss the positive-P function and show that its discretization can be used to treat the problem of diverging trajectories. We study the dissipative long-range transverse-field Ising chain and show that the long-time dynamics of local observables is well described by a semiclassical approximation of the interactions.
PACS: 03.65.Sq – Semiclassical theories and applications / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 03.65.Yz – Decoherence; open systems; quantum statistical methods
© EPLA, 2015