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dc.contributor.author
Martin, John
dc.contributor.author
Garcia-Mata, Ignacio
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dc.contributor.author
Giraud, Olivier
dc.contributor.author
Georgeot, Bertrand
dc.date.available
2023-01-31T18:01:41Z
dc.date.issued
2010-10
dc.identifier.citation
Martin, John; Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand; Multifractal wave functions of simple quantum maps; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 82; 4; 10-2010; 46206-46219
dc.identifier.issn
1539-3755
dc.identifier.uri
http://hdl.handle.net/11336/186332
dc.description.abstract
We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, and absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Physical Society
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Multifractales
dc.subject
Localizacion
dc.subject.classification
Física de los Materiales Condensados
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dc.subject.classification
Ciencias Físicas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Multifractal wave functions of simple quantum maps
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-04-23T19:24:28Z
dc.journal.volume
82
dc.journal.number
4
dc.journal.pagination
46206-46219
dc.journal.pais
Estados Unidos
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dc.description.fil
Fil: Martin, John. Université de Liège; Bélgica
dc.description.fil
Fil: Garcia-Mata, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
dc.description.fil
Fil: Giraud, Olivier. Centre National de la Recherche Scientifique; Francia. Laboratoire Physique Theorique Et Modeles Statistique; Francia
dc.description.fil
Fil: Georgeot, Bertrand. Centre National de la Recherche Scientifique; Francia
dc.journal.title
Physical Review E: Statistical, Nonlinear and Soft Matter Physics
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.82.046206
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1103/PhysRevE.82.046206
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