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...

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Detalles Bibliográficos
Autores principales: García, Javier, Rossignoli, Raúl
Formato: Articulo Preprint
Lenguaje:Español
Publicado: 2017
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Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/75424
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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.