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- W3100350050 abstract "We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, |zmin| ⩽ |z| ⩽ |zmax|. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius r. We prove that if the moduli converge to r = |zmax| then the sequence of eigenstates is associated with a fixed phase space measure ρmax. The same holds for sequences with eigenvalue moduli converging to |zmin|, with a different limit measure ρmin. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius |zmin| < r < |zmax| there is no unique limit measure, and we identify some families of eigenstates with precise self-similar properties." @default.
- W3100350050 created "2020-11-23" @default.
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- W3100350050 date "2008-09-29" @default.
- W3100350050 modified "2023-10-14" @default.
- W3100350050 title "On the resonance eigenstates of an open quantum baker map" @default.
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- W3100350050 doi "https://doi.org/10.1088/0951-7715/21/11/007" @default.
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