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Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model. (arXiv:1712.04152v1 [math-ph])

来源于:arXiv
The purpose of the present paper is to study the exceptional eigenvalues of the asymmetric quantum Rabi models (AQRM), specifically, to determine the degeneracy of the exceptional eigenstates. Exceptional eigenvalues are labelled by certain integers and are considered to be remains of the eigenvalues of the uncoupled bosonic mode (i.e. the quantum harmonic oscillator). There are two kind of exceptional eigenvalues of the Hamiltonian $H^{\epsilon}_{\text{Rabi}}$ of the AQRM: the Juddian, associated with polynomial, or quasi-exact, eigensolutions, and the non-Juddian exceptional. Here, $H^{\epsilon}_{\text{Rabi}}$ is defined by adding the fluctuation term $\epsilon \sigma_x$, with real $\epsilon$ and $\sigma_x$ being the Pauli matrix, to the Hamiltonian of the quantum Rabi model (QRM), breaking its $\mathbb{Z}_2$-symmetry. An eigenvalue which is not exceptional is called regular and is always non-degenerate. We describe the constraint relations for allowing the model to have exceptional 查看全文>>