Regularity of Bound States

Abstract

We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator $H$, with respect to an auxiliary operator $A$ that is conjugate to $H$ in the sense of Mourre. We work within the framework of singular Mourre theory which enables us to deal with confined massless Pauli-Fierz models, our primary example, and many-body AC-Stark Hamiltonians. In the simpler context of regular Mourre theory our results boils down to an improvement of results obtained recently in \cite{CGH}.

70 pages

References in corpus (4)

• Another Return of 'Return to Equilibrium'
• Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
• Second order perturbation theory for embedded eigenvalues
• Regularity of Eigenstates in Regular Mourre Theory

Cited by in corpus (9)

• Second order perturbation theory for embedded eigenvalues
• The translation invariant massive Nelson model: III. Asymptotic completeness below the two-boson threshold
• Regularity of Eigenstates in Regular Mourre Theory
• Propagation estimates in the one-commutator theory
• Bands of pure a.c. spectrum for lattice Schr{ö}dinger operators with a more general long range condition. Part I
• Spectral deformation for two-body dispersive systems with e.g. the Yukawa potential
• Fully Coupled Pauli-Fierz Systems at Zero and Positive Temperature
• Existence and regularity of propagators for multi-particle Schrödinger equations in external fields
• Persistence of embedded eigenvalues