The threshold effects for a family of Friedrichs models under rank one perturbations. (English) Zbl 1115.81023
Summary: A family of Friedrichs models under rank one perturbations \(h_\mu (p)\), \(p\in(-\pi,\pi]^3\), \(\mu>0\), associated to a system of two particles on the three-dimensional lattice \(\mathbb{Z}^3\) is considered. We prove the existence of a unique eigenvalue below the bottom of the essential spectrum of \(h_\mu(p)\) for all non-trivial values of \(p\) under the assumption that \(h_\mu(0)\) has either a threshold energy resonance (virtual level) or a threshold eigenvalue. The threshold energy expansion for the Fredholm determinant associated to a family of Friedrichs models is also obtained.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
Keywords:
energy resonance; pair non-local potentials; conditionally negative definite functions; eigenvalueReferences:
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