Spectrum and normal modes of non-hermitian quadratic boson operators
We analyze the spectrum and normal mode representation of general quadratic bosonic formsHnot necessarily hermitian. It is shown that in the one-dimensional case such forms exhibit either an harmonic regime where bothHandH^†have a discrete spectrum with biorthogonal eigenstates, and a coherent-like...
Guardado en:
| Autores principales: | , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Español |
| Publicado: |
2017
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/75424 |
| Aporte de: |
| Sumario: | We analyze the spectrum and normal mode representation of general quadratic bosonic formsHnot necessarily hermitian. It is shown that in the one-dimensional case such forms exhibit either an harmonic regime where bothHandH^†have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where eitherHorH†have a continuous complex two-fold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Non-diagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension toN-dimensional quadratic systems is as well discussed. |
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