Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Abstract

We show how quasiprobability distribution functions defined over $N^2$-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin tunneling effects. This particular approach is then applied to the Lipkin-Meshkov-Glick model in order to obtain the time evolution of the discrete Husimi function, and as a by-product the energy gap for a symmetric combination of ground and first excited states. Moreover, we also show how an angle-based potential approach can be efficiently employed to explain qualitatively certain features of the energy gap in terms of a spin tunneling. Entropy functionals are also discussed in this context. Such results reinforce not only the formalism per se but also the possibility of some future potential applications in other branches of physics.

7 pages, 8 figures, title modified, new setences and references included, to appear in Physical Review A

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• Spin squeezing and entanglement for arbitrary spin
• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Quasiprobability distributions for quantum-optical coherence and beyond
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• Optimal quantum channels
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