Parity-time symmetry broken by point-group symmetry

We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficient...

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Detalles Bibliográficos
Autores principales: Fernández, Francisco Marcelo, García, Javier
Formato: Articulo
Lenguaje:Inglés
Publicado: 2014
Materias:
Química
Eigenvalues
Phase transitions
Perturbation theory
Polynomials
Signal generators
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/102510
https://ri.conicet.gov.ar/11336/33104
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-102510
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Química
Eigenvalues
Phase transitions
Perturbation theory
Polynomials
Signal generators
spellingShingle Química
Eigenvalues
Phase transitions
Perturbation theory
Polynomials
Signal generators
Fernández, Francisco Marcelo
García, Javier
Parity-time symmetry broken by point-group symmetry
topic_facet Química
Eigenvalues
Phase transitions
Perturbation theory
Polynomials
Signal generators
description We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy2 exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
format Articulo
Articulo
author Fernández, Francisco Marcelo
García, Javier
author_facet Fernández, Francisco Marcelo
García, Javier
author_sort Fernández, Francisco Marcelo
title Parity-time symmetry broken by point-group symmetry
title_short Parity-time symmetry broken by point-group symmetry
title_full Parity-time symmetry broken by point-group symmetry
title_fullStr Parity-time symmetry broken by point-group symmetry
title_full_unstemmed Parity-time symmetry broken by point-group symmetry
title_sort parity-time symmetry broken by point-group symmetry
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/102510
https://ri.conicet.gov.ar/11336/33104
work_keys_str_mv AT fernandezfranciscomarcelo paritytimesymmetrybrokenbypointgroupsymmetry
AT garciajavier paritytimesymmetrybrokenbypointgroupsymmetry
bdutipo_str Repositorios
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