Spectral properties of the singular Friedrichs–Lee Hamiltonian
Paolo Facchi, Marilena Ligabò, Davide Lonigro
Abstract
We show that the Friedrichs–Lee model, which describes the one-excitation sector of a two-level atom interacting with a structured boson field, can be generalized to singular atom–field couplings. We provide a characterization of its spectrum and resonances and discuss the inverse spectral problem.
Topics & Concepts
Spectral propertiesHamiltonian (control theory)BosonPhysicsInverseCharacterization (materials science)Spectrum (functional analysis)Mathematical physicsMathematicsEigenvalues and eigenvectorsSpectral theoryQuantum mechanicsHamiltonian systemSpectral analysisInverse problemHilbert spaceGeneralized inverseMathematical analysisAtom (system on chip)Singular spectrum analysisCold Atom Physics and Bose-Einstein CondensatesSpectral Theory in Mathematical PhysicsQuantum Mechanics and Non-Hermitian Physics