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Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

Minoru Horibe·Akiyoshi Takami·Takaaki Hashimoto·Akihisa Hayashi
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Abstract

In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase space" is a lattice with $N^2$ sites, we get different results depending on whether $N$ is odd or even. Under the new condition, the Wigner function is determined if $N$ is an odd number, but it does not exist if $N$ is even.

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Minoru Horibe, Akiyoshi Takami, Takaaki Hashimoto, Akihisa Hayashi. 2001-08-10. Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice. https://doi.org/10.1103/physreva.65.032105

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