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  • Wigner function statistics in classically chaotic systems
    Horvat, Martin ; Prosen, Tomaž, 1970-
    We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function ... probability distribution P(w) = (1/V) (w - W(x))dx, which has, by definition, fixed first and second moments.In particular, we concentrate on relaxation of time-evolving quantum states in terms of W(x), starting from a coherent state. We have shown that for a classically chaotic quantum counterpart the distribution P(w) in the semiclassical limit becomes a Gaussian distribution that is fully determined by the first two moments. Numerical simulations have been performed for the quantum sawtooth map and the quantized kicked top. In a quantum system with Hilbert space dimension N(~1ž) the transition of P(w) to a Gaussian distribution was observed at times t log N. In addition, it has been shown that the statistics of Wigner functions of propagator eigenstates is Gaussian as well in the classically fully chaotic regime. We have also studied the structure of the nodal cells of the Wigner function, in particular the distribution of intersection points between the zero manifold and arbitrary straight lines.
    Vir: Journal of physics. A, Mathematical and general. - ISSN 0305-4470 (36, 2003, str. 4015-4034)
    Vrsta gradiva - članek, sestavni del
    Leto - 2003
    Jezik - angleški
    COBISS.SI-ID - 1628772

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