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Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations

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Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations

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dc.contributor.author Bader, Philipp es_ES
dc.contributor.author Blanes Zamora, Sergio es_ES
dc.date.accessioned 2018-03-23T13:33:40Z
dc.date.available 2018-03-23T13:33:40Z
dc.date.issued 2011 es_ES
dc.identifier.issn 1539-3755 es_ES
dc.identifier.uri http://hdl.handle.net/10251/99668
dc.description.abstract [EN] We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using fast Fourier transforms. Splitting the system into the quantum harmonic-oscillator problem and the remaining part allows us to get higher accuracies in many cases, but it requires us to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build methods that combine the advantages of using Fourier methods while solving the time-dependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition). © 2011 American Physical Society. es_ES
dc.description.sponsorship We would like to acknowledge the referees for their careful reading and suggestions. The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032. The work of S. B. has also been partially supported by Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03 (cofinanced by the ERDF of the European Union).
dc.language Inglés es_ES
dc.publisher American Physical Society es_ES
dc.relation GENERALITAT VALENCIANA/GV/2009/032 es_ES
dc.relation Ministerio de Ciencia e Innovación/MTM2010-18246-C03-02 es_ES
dc.relation.ispartof Physical Review E es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Coordinate space es_ES
dc.subject Dinger equation es_ES
dc.subject Fourier methods es_ES
dc.subject Fourier techniques es_ES
dc.subject Gross-Pitaevskii equation es_ES
dc.subject Harmonic oscillators es_ES
dc.subject Harmonic potential es_ES
dc.subject Hermite basis functions es_ES
dc.subject Numerical integrations es_ES
dc.subject Potential trap es_ES
dc.subject Small perturbations es_ES
dc.subject Splitting method es_ES
dc.subject Strong nonlinearity es_ES
dc.subject Time-dependent es_ES
dc.subject Bose-Einstein condensation es_ES
dc.subject Control nonlinearities es_ES
dc.subject Harmonic analysis es_ES
dc.subject Harmonic functions es_ES
dc.subject Integration es_ES
dc.subject Numerical methods es_ES
dc.subject Oscillators (mechanical) es_ES
dc.subject Fast Fourier transforms es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1103/PhysRevE.83.046711 es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bader, P.; Blanes Zamora, S. (2011). Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations. Physical Review E. 83(4):46711-1-46711-11. doi:10.1103/PhysRevE.83.046711 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1103/PhysRevE.83.046711 es_ES
dc.description.upvformatpinicio 46711-1 es_ES
dc.description.upvformatpfin 46711-11 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 83 es_ES
dc.description.issue 4 es_ES
dc.identifier.pmid 21599338
dc.relation.pasarela S\210383 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES


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