Continuous phase-space methods on discrete phase spaces

Abstract

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.

10 pages, 4 figures

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Cited by in corpus (2)

• Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems
• Quenches near criticality of the quantum Ising chain---power and limitations of the discrete truncated Wigner approximation