Absence of positive eigenvalues for hard-core \(N\)-body systems

DOI10.1007/s00023-013-0309-xzbMath1304.81163OpenAlexW2131735936MaRDI QIDQ481795

Kenichi Ito, Erik Skibsted

Publication date: 15 December 2014

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00023-013-0309-x

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Atomic physics (81V45) Many-body theory; quantum Hall effect (81V70) Molecular physics (81V55)

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Pauli-Fierz type operators with singular electromagnetic potentials on general domains, Upper bounds of local electronic densities in molecules, Decay of eigenfunctions of elliptic PDE's. I, New methods in spectral theory of N-body Schrödinger operators

Cites Work

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• Commutators, \(C_{0}\)-semigroups and resolvent estimates
• Exponential bounds and semi-finiteness of point spectrum for N-body Schrödinger operators
• Asymptotic completeness for N-body short-range quantum systems: A new proof
• Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
• Propagation estimates for \(N\)-body Schrödinger operators
• The commutator method for form-relatively compact perturbations
• Asymptotic completeness of long-range \(N\)-body quantum systems
• Recent work on sharp estimates in second-order elliptic unique continuation problems
• Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
• On the absence of positive eigenvalues for one-body Schrödinger operators
• Scattering theory for Riemannian Laplacians
• Radiation conditions and scattering theory for \(N\)-particle Hamiltonians
• Absence of embedded eigenvalues for Riemannian Laplacians
• Effective limiting absorption principles, and applications
• ABSENCE OF POSITIVE EIGENVALUES FOR HARD-CORE N-BODY SYSTEMS
• Spectral Analysis of N-Body Systems Coupled to a Bosonic Field
• N-BODY HAMILTONIANS WITH HARD-CORE INTERACTIONS
• \(C_0\)-groups, commutator methods and spectral theory of \(N\)-body Hamiltonians