Classical transients and the support of open quantum maps

The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller - the set of nonescaping orbits in the future and past evol...

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Autores principales:	Carlo, Gabriel Gustavo, Wisniacki, Diego A., Ermann, Leonardo
Publicado:	2013
Materias:	Asymptotic properties Eigenvalue distributions Evolution operator Invariant objects Numerical evidence Open maps Open quantum systems Periodic orbits Quantum maps Scattering systems Semiclassical theories Quantum electronics Quantum optics Eigenvalues and eigenfunctions article chemical model computer simulation quantum theory statistical model Computer Simulation Models, Chemical Models, Statistical Quantum Theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n1_p_Carlo http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Carlo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15393755_v87_n1_p_Carlo
record_format	dspace
spelling	paper:paper_15393755_v87_n1_p_Carlo2023-06-08T16:20:56Z Classical transients and the support of open quantum maps Carlo, Gabriel Gustavo Wisniacki, Diego A. Ermann, Leonardo Asymptotic properties Eigenvalue distributions Evolution operator Invariant objects Numerical evidence Open maps Open quantum systems Periodic orbits Quantum maps Scattering systems Semiclassical theories Quantum electronics Quantum optics Eigenvalues and eigenfunctions article chemical model computer simulation quantum theory statistical model Computer Simulation Models, Chemical Models, Statistical Quantum Theory The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller - the set of nonescaping orbits in the future and past evolution - is the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps, which share the same asymptotic properties but differ in their short-time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems. We provide an interpretation of the results in order to have hints about them. © 2013 American Physical Society. Fil:Carlo, G.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wisniacki, D.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Ermann, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n1_p_Carlo http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Carlo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Asymptotic properties Eigenvalue distributions Evolution operator Invariant objects Numerical evidence Open maps Open quantum systems Periodic orbits Quantum maps Scattering systems Semiclassical theories Quantum electronics Quantum optics Eigenvalues and eigenfunctions article chemical model computer simulation quantum theory statistical model Computer Simulation Models, Chemical Models, Statistical Quantum Theory
spellingShingle	Asymptotic properties Eigenvalue distributions Evolution operator Invariant objects Numerical evidence Open maps Open quantum systems Periodic orbits Quantum maps Scattering systems Semiclassical theories Quantum electronics Quantum optics Eigenvalues and eigenfunctions article chemical model computer simulation quantum theory statistical model Computer Simulation Models, Chemical Models, Statistical Quantum Theory Carlo, Gabriel Gustavo Wisniacki, Diego A. Ermann, Leonardo Classical transients and the support of open quantum maps
topic_facet	Asymptotic properties Eigenvalue distributions Evolution operator Invariant objects Numerical evidence Open maps Open quantum systems Periodic orbits Quantum maps Scattering systems Semiclassical theories Quantum electronics Quantum optics Eigenvalues and eigenfunctions article chemical model computer simulation quantum theory statistical model Computer Simulation Models, Chemical Models, Statistical Quantum Theory
description	The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller - the set of nonescaping orbits in the future and past evolution - is the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps, which share the same asymptotic properties but differ in their short-time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems. We provide an interpretation of the results in order to have hints about them. © 2013 American Physical Society.
author	Carlo, Gabriel Gustavo Wisniacki, Diego A. Ermann, Leonardo
author_facet	Carlo, Gabriel Gustavo Wisniacki, Diego A. Ermann, Leonardo
author_sort	Carlo, Gabriel Gustavo
title	Classical transients and the support of open quantum maps
title_short	Classical transients and the support of open quantum maps
title_full	Classical transients and the support of open quantum maps
title_fullStr	Classical transients and the support of open quantum maps
title_full_unstemmed	Classical transients and the support of open quantum maps
title_sort	classical transients and the support of open quantum maps
publishDate	2013
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n1_p_Carlo http://hdl.handle.net/20.500.12110/paper_15393755_v87_n1_p_Carlo
work_keys_str_mv	AT carlogabrielgustavo classicaltransientsandthesupportofopenquantummaps AT wisniackidiegoa classicaltransientsandthesupportofopenquantummaps AT ermannleonardo classicaltransientsandthesupportofopenquantummaps
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Classical transients and the support of open quantum maps

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