Inverse problems, trace formulae for discrete Schrödinger operators

DOI10.1007/s00023-011-0141-0zbMath1250.81124arXiv1103.2193OpenAlexW2041224997MaRDI QIDQ425125

Hiroshi Isozaki, Evgeny L. Korotyaev

Publication date: 7 June 2012

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

Full work available at URL: https://arxiv.org/abs/1103.2193

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse scattering problems in quantum theory (81U40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (max. 100)

Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices ⋮ Microlocal properties of scattering matrices ⋮ Essential spectrum of the discrete Laplacian on a perturbed periodic graph ⋮ Spectral and scattering theory for Schrödinger operators on perturbed topological crystals ⋮ Modified wave operators for discrete Schrödinger operators with long-range perturbations ⋮ Long-range scattering for discrete Schrödinger operators ⋮ The regularized trace of Sturm–Liouville problem with discontinuities at two points ⋮ Inverse resonance problem for Jacobi operators on a half-lattice ⋮ Gelfand's inverse problem for the graph Laplacian ⋮ Branching form of the resolvent at thresholds for multi-dimensional discrete Laplacians ⋮ Phase recovery from phaseless scattering data for discrete Schrödinger operators ⋮ Schrödinger operators with guided potentials on periodic graphs ⋮ Trace formulas for a discrete Schrödinger operator ⋮ Trace formulas for time periodic complex Hamiltonians on lattice ⋮ Inverse scattering theory for discrete Schrödinger operators on the hexagonal lattice ⋮ Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice ⋮ Trace formulas for Schrödinger operators on a lattice ⋮ Coherent states for graphene under the interaction of crossed electric and magnetic fields ⋮ Long-range scattering theory for discrete Schrödinger operators on graphene ⋮ Spectral estimates for Schrödinger operators on periodic discrete graphs ⋮ Limiting absorption principle on L p-spaces and scattering theory ⋮ A Rellich type theorem for discrete Schrödinger operators ⋮ Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph ⋮ Scattering on periodic metric graphs ⋮ Bands of pure absolutely continuous spectrum for lattice Schrödinger operators with a more general long range condition ⋮ Inverse scattering for Schrödinger operators on perturbed lattices ⋮ Analyticity properties of the scattering matrix for matrix Schrödinger operators on the discrete line ⋮ Resonances for Euler-Bernoulli operator on the half-line ⋮ Schrödinger operators on periodic discrete graphs ⋮ A remark on the Mourre theory for two body Schrödinger operators ⋮ Laplacians on periodic graphs with guides ⋮ Eigenvalues of periodic difference operators on lattice octants ⋮ Hypergeometric expression for the resolvent of the discrete Laplacian in low dimensions ⋮ On a continuum limit of discrete Schrödinger operators on square lattice ⋮ Spectral properties of Schrödinger operators on perturbed lattices ⋮ On the Solvability of the Discrete Conductivity and Schrödinger Inverse Problems ⋮ Inverse scattering at a fixed energy for discrete Schrödinger operators on the square lattice ⋮ Spectral features of two-particle Schrödinger operator on \(d\)-dimensional lattice ⋮ Schrödinger operators with potential waveguides on periodic graphs ⋮ Trace formulas for Schrödinger operators with complex potentials ⋮ Trace formulas for Schrödinger operators on periodic graphs ⋮ Uniform bounds of discrete Birman–Schwinger operators ⋮ Spectral asymptotics at thresholds for a Dirac-type operator on \(\mathbb{Z}^2\) ⋮ Spectral and scattering theory for topological crystals perturbed by infinitely many new edges

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A global uniqueness theorem for an inverse boundary value problem
• On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\)
• A trace formula and high-energy spectral asymptotics for the perturbed Landau Hamiltonian
• The threshold effects for the two-particle Hamiltonians on lattices
• Reconstructions from boundary measurements
• Absence of singular continuous spectrum for certain self-adjoint operators
• Asymptotic properties of solutions of differential equations with simple characteristics
• Inverse problem of quantum scattering theory. II
• The \(\xi\) function
• A trace formula for multidimensional Schrödinger operators
• Absolute summability of the trace relation for certain Schrödinger operators
• Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds
• An asymptotic behavior of the S-matrix and the inverse scattering problem
• The number of bound states for a discrete Schrödinger operator on {\bb Z}^N, N\geq1 , lattices
• The $ \bar\partial$-equation in the multidimensional inverse scattering problem
• Une formule de traces pour l'opérateur de Schrödinger dans $\mathbb{R}^3$
• ON THE SPECTRAL PROPERTIES OF DISCRETE SCHRÖDINGER OPERATORS
• Trace Formulae and High Energy Asymptotics for the Stark Operator
• The geometrical approach to multidimensional inverse scattering
• The number of eigenvalues of three-particle Schrödinger operators on lattices
• On the theory of linear equations and Fredholm determinants
• \(C_0\)-groups, commutator methods and spectral theory of \(N\)-body Hamiltonians
• A trace formula for discrete Schrödinger operators

This page was built for publication: Inverse problems, trace formulae for discrete Schrödinger operators