Continuous phase-space methods on discrete phase spaces

Bojan Žunkovič

doi:10.1209/0295-5075/112/10003

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arXiv · 1508.00135

Continuous phase-space methods on discrete phase spaces

Bojan Žunkovič

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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.

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Bojan Žunkovič. 2015-08-01. Continuous phase-space methods on discrete phase spaces. https://doi.org/10.1209/0295-5075%2F112%2F10003

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