PMID: 22587157May 17, 2012Paper

Short periodic orbit approach to resonances and the fractal Weyl law

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Juan M PedrosaM Novaes

Abstract

We investigate the properties of the semiclassical short periodic orbit approach for the study of open quantum maps that was recently introduced [Novaes, Pedrosa, Wisniacki, Carlo, and Keating, Phys. Rev. E 80, 035202(R) (2009)]. We provide solid numerical evidence, for the paradigmatic systems of the open baker and cat maps, that by using this approach the dimensionality of the eigenvalue problem is reduced according to the fractal Weyl law. The method also reproduces the projectors |ψ(n)(R)><ψ(n)(L)|, which involves the right and left states associated with a given eigenvalue and is supported on the classical phase-space repeller.

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Citations

Feb 26, 2016·The Journal of Physical Chemistry. a·F RevueltaF Borondo
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A PotzuweitM Zworski
May 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F RevueltaE Vergini
Feb 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Moritz Schönwetter, Eduardo G Altmann
Aug 31, 2016·Physical Review. E·Gabriel G CarloF Borondo
May 16, 2018·Physical Review. E·Carlos A PradoF Borondo
Oct 24, 2019·Physical Review. E·Agustín M BilenOlivier Giraud
Mar 15, 2020·Physical Review. E·Gabriel G Carlo, F Borondo
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Gabriel G CarloF Borondo
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Leonardo ErmannMarcos Saraceno
May 20, 2021·Physical Review. E·Konstantin ClaußRoland Ketzmerick

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