Spectral Analysis of N-Body Systems Coupled to a Bosonic Field

DOI10.1142/S0129055X9800032XzbMath0945.81008OpenAlexW2160832916MaRDI QIDQ4235696

Erik Skibsted

Publication date: 12 October 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129055x9800032x

zbMATH Keywords

thresholdseigenvaluesspectral theoryquantum electrodynamicssingular spectrumspin-boson modelelectron-boson modelnonrelativistic atom

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Electromagnetic interaction; quantum electrodynamics (81V10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (35)

Spectral theory of time-periodic many-body systems ⋮ On the absence of excited eigenstates of atoms in QED ⋮ Spectral Properties for Hamiltonians of Weak Interactions ⋮ CONSTRUCTION OF METASTABLE STATES IN QUANTUM ELECTRODYNAMICS ⋮ Spectral theory for a mathematical model of the weak interaction. I: The decay of the intermediate vector bosons \(W^{\pm}\) ⋮ On the spectral analysis of quantum field Hamiltonians ⋮ Regularity of eigenstates in regular Mourre theory ⋮ Cherenkov radiation with massive bosons and quantum friction ⋮ Second order perturbation theory for embedded eigenvalues ⋮ Asymptotic completeness for the massless spin-boson model ⋮ Absence of positive eigenvalues for hard-core \(N\)-body systems ⋮ Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED ⋮ Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation ⋮ SPECTRAL RENORMALIZATION GROUP AND LOCAL DECAY IN THE STANDARD MODEL OF NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS ⋮ REGULARITY OF BOUND STATES ⋮ Rayleigh scattering at atoms with dynamical nuclei ⋮ Spectral analysis of the spin-boson Hamiltonian with two photons for arbitrary coupling ⋮ On Rayleigh scattering in non-relativistic quantum electrodynamics ⋮ Spectral theory for the standard model of non-relativistic QED ⋮ Spectral theory of Pauli-Fierz operators. ⋮ On the Mourre estimates for Floquet Hamiltonians ⋮ Commutators, \(C_{0}\)-semigroups and resolvent estimates ⋮ Minimal photon velocity bounds in non-relativistic quantum electrodynamics ⋮ REMARKS ON THE GROUND STATE ENERGY OF THE SPIN-BOSON MODEL: AN APPLICATION OF THE WIGNER–WEISSKOPF MODEL ⋮ ON THE SCATTERING THEORY OF MASSLESS NELSON MODELS ⋮ Ground state transition for two-level system coupled with Bose field ⋮ Return to equilibrium ⋮ Asymptotic electromagnetic fields in models of quantum-mechanical matter interacting with the quantized radiation field ⋮ Radiation and Scattering in Non-relativistic Quantum Electrodynamics ⋮ Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians ⋮ Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field Hamiltonians ⋮ On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case ⋮ Spectral theory of massless Pauli-Fierz models ⋮ Differential equations of quantum mechanics ⋮ Fully coupled Pauli-Fierz systems at zero and positive temperature

Cites Work

• Asymptotic completeness for N-body short-range quantum systems: A new proof
• A new proof of the Mourre estimate
• Perturbation of embedded eigenvalues in the generalized N-body problem
• Spectral analysis of N-body Schrödinger operators
• Absence of singular continuous spectrum for certain self-adjoint operators
• Propagation estimates for \(N\)-body Schrödinger operators
• The commutator method for form-relatively compact perturbations
• Asymptotic completeness of long-range \(N\)-body quantum systems
• Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory

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