Is space-time symmetry a suitable generalization of parity-time symmetry?

Authors
Amore, Paolo; Fernández, Francisco Marcelo; Garcia, Javier
Publication Year
2014
Language
English
Format
article
Status
Published version
Description
We discuss space-time symmetric Hamiltonian operators of the form H = H0 + igH ′ , where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G′ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g < gc , where gc is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.
Fil: Amore, Paolo . Universidad de Colima; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Subject
PT-SYMMETRY
SPACE-TIME SYMMETRY
NON-HERMITIAN HAMILTONIAN
MULTIDIMENSIONAL SYSTEM
Física Atómica, Molecular y Química
Ciencias Físicas
CIENCIAS NATURALES Y EXACTAS
Access level
Embargoed access
License
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/5157