On the resonance eigenstates of an open quantum baker map

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dc.creatorKeating, J. P.
dc.creatorNonnenmacher, S.
dc.creatorNovaes, M.
dc.creatorSieber, M.
dc.date2008-06-10
dc.date2008-10-03
dc.date.accessioned2026-07-07T10:06:58Z
dc.date.available2026-07-07T10:06:58Z
dc.descriptionWe 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, $|z_{min}|\leq |z|\leq |z_{max}|$. 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 $r=|z_{max}|$, then the sequence of eigenstates converges to a fixed phase space measure $ρ_{max}$. The same holds for sequences with eigenvalue moduli converging to $|z_{min}|$, with a different limit measure $ρ_{min}$. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius $|z_{min}|< r < |z_{max}|$, we identify families of eigenstates with precise self-similar properties.
dc.description32 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0806.1678
dc.identifierhttp://arxiv.org/abs/0806.1678
dc.identifierNonlinearity 21, 2591 (2008)
dc.identifierdoi:10.1088/0951-7715/21/11/007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170473
dc.subjectChaotic Dynamics
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.titleOn the resonance eigenstates of an open quantum baker map
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