Spectrum and normal modes of non-Hermitian quadratic boson operators

GARCIA, JAVIER; ROSSIGNOLI, R.

Physical Review A

American Physical Society

Año: 2017 vol. 96

2469-9926

We analyze the spectrum and normal-mode representation of general quadratic bosonic forms H not necessarilyHermitian. It is shown that, in the one-dimensional case, such forms exhibit either a harmonic regime where both?H and H have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where either H?or H have a continuous complex twofold degenerate spectrum, while its adjoint has no convergent eigenstates.These regimes reflect the nature of the pertinent normal boson operators. Nondiagonalizable cases as well criticalboundary sectors separating these regimes are also analyzed. The extension to N -dimensional quadratic systemsis also discussed.