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arXiv · 1404.4603

Complex modes in unstable quadratic bosonic forms

R. Rossignoli·A. M. Kowalski
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Abstract

We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to non-hermitian coordinates and momenta and are associated with complex frequencies. As application, we examine a bosonic version of a BCS-like pairing Hamiltonian, which, in contrast with the fermionic case, is stable just for limited values of the gap parameter and requires the use of the present extended treatment for a general diagonal representation. The dynamical stability of such forms and the occurrence of non-diagonalizable cases are also discussed.

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R. Rossignoli, A. M. Kowalski. 2014-04-17. Complex modes in unstable quadratic bosonic forms. https://doi.org/10.1103/physreva.72.032101

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