Abstract.
The Wigner and Husimi distributions are the usual phase space representations of a quantum state. The Wigner distribution has structures of order ħ2. On the other hand, the Husimi distribution is a Gaussian smearing of the Wigner function on an area of size ħ and then, it only displays structures of size ħ. We have developed a phase space representation which results a Gaussian smearing of the Wigner function on an area of size ħσ, with σ≥1. Within this representation, the Husimi and Wigner functions are recovered when σ=1 and \( \sigma \gtrsim 2 \) respectively. We treat the application of this intermediate representation to explore the semiclassical limit of quantum mechanics. In particular we show how this representation uncover semiclassical hyperbolic structures of chaotic eigenstates.
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Rivas, A., Vergini, E. & Wisniacki, D. Smoothed Wigner functions: a tool to resolve semiclassical structures. Eur. Phys. J. D 32, 355–359 (2005). https://doi.org/10.1140/epjd/e2004-00189-8
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DOI: https://doi.org/10.1140/epjd/e2004-00189-8