Is space-time symmetry a suitable generalization of parity-time symmetry?
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 representation...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/5157 |
| Acceso en línea: | http://hdl.handle.net/11336/5157 |
| Access Level: | acceso embargado |
| Palabra clave: | Pt-Symmetry Space-Time Symmetry Non-Hermitian Hamiltonian Multidimensional System https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| Sumario: | 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. |
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