The geometrical basis of PT symmetry
We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and p...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/12995 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/12995 |
| Access Level: | acceso abierto |
| Palabra clave: | 535 Non-hermitian hamiltonians Complex periodic potentials Quantum-mechanics Pt-symmetry Eigenvalues Equivalent Scattering Spectra Óptica (Física) 2209.19 Óptica Física |
| Sumario: | We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system. |
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