Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices

We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by cla...

Descripción completa

Detalles Bibliográficos
Autores: Bajārs, Jānis, Archilla, Juan F. R.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/144463
Acceso en línea:https://hdl.handle.net/11441/144463
https://doi.org/10.3390/math10193460
Access Level:acceso abierto
Palabra clave:semi-classical Hamiltonian dynamics
splitting methods
symplectic integrators
lattice models
charge transfer
intrinsic localized modes
discrete breathers
id ES_ec4ae7f9c2c0fb63002c4f3e7eeeaec9
oai_identifier_str oai:idus.us.es:11441/144463
network_acronym_str ES
network_name_str España
repository_id_str
spelling Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear LatticesBajārs, JānisArchilla, Juan F. R.semi-classical Hamiltonian dynamicssplitting methodssymplectic integratorslattice modelscharge transferintrinsic localized modesdiscrete breathersWe propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystalMinisterio de Ciencia, Innovación y Universidades PID2019-109175GB-C22Junta de Andalucía US-1380977MDPIFísica Aplicada IMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaJunta de Andalucía2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/144463https://doi.org/10.3390/math10193460reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematics, 10 (19).PID2019-109175GB-C22US-1380977https://www.mdpi.com/2227-7390/10/19/3460info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1444632026-06-17T12:51:07Z
dc.title.none.fl_str_mv Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
title Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
spellingShingle Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
Bajārs, Jānis
semi-classical Hamiltonian dynamics
splitting methods
symplectic integrators
lattice models
charge transfer
intrinsic localized modes
discrete breathers
title_short Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
title_full Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
title_fullStr Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
title_full_unstemmed Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
title_sort Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
dc.creator.none.fl_str_mv Bajārs, Jānis
Archilla, Juan F. R.
author Bajārs, Jānis
author_facet Bajārs, Jānis
Archilla, Juan F. R.
author_role author
author2 Archilla, Juan F. R.
author2_role author
dc.contributor.none.fl_str_mv Física Aplicada I
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
Junta de Andalucía
dc.subject.none.fl_str_mv semi-classical Hamiltonian dynamics
splitting methods
symplectic integrators
lattice models
charge transfer
intrinsic localized modes
discrete breathers
topic semi-classical Hamiltonian dynamics
splitting methods
symplectic integrators
lattice models
charge transfer
intrinsic localized modes
discrete breathers
description We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/144463
https://doi.org/10.3390/math10193460
url https://hdl.handle.net/11441/144463
https://doi.org/10.3390/math10193460
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematics, 10 (19).
PID2019-109175GB-C22
US-1380977
https://www.mdpi.com/2227-7390/10/19/3460
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869423302433308672
score 15,301603

Similares en LA Referencia