Chaos-revealing multiplicative representation of quantum eigenstates

Abstract : The quantization of the two-dimensional toric and spherical phase spaces is considered in analytic coherent state representations. Every pure quantum state admits there a finite multiplicative parametrization by the zeros of its Husimi function. For eigenstates of quantized systems, this description explicitly reflects the nature of the underlying classical dynamics: in the semiclassical regime, the distribution of the zeros in the phase space becomes one-dimensional for integrable systems, and highly spread out (conceivably uniform) for chaotic systems. This multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems.
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Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 1990, 23, pp.1765-1774. 〈10.1088/0305-4470/23/10/017〉
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P. Leboeuf, André Voros. Chaos-revealing multiplicative representation of quantum eigenstates. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 1990, 23, pp.1765-1774. 〈10.1088/0305-4470/23/10/017〉. 〈hal-00164337〉

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