Husimi-Wigner representation of chaotic eigenstates

Abstract

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi-Wigner reresentation. It occupies an intermediate ground between drastic suppression of nonclassical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of chaotic Hamiltonians. The individual two-dimensional Wigner functions resemble those of semiclassically quantized states, but the regular ring pattern is broken by dislocations.

21 pages, 7 figures (6 color figures), submitted to Proc. R. Soc. A

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Cited by in corpus (4)

• The physics and applications of strongly coupled plasmas levitated in electrodynamic traps
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Phase space formulation of the Abelian and non-Abelian quantum geometric tensor
• Husimi function for electrons moving in magnetic fields