On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension

DOI10.1063/1.3005597zbMath1159.81336arXiv0804.1963OpenAlexW2166202717MaRDI QIDQ3624645

Dmitry E. Pelinovsky, Atanas G. Stefanov

Publication date: 30 April 2009

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

Full work available at URL: https://arxiv.org/abs/0804.1963

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Discrete version of topics in analysis (39A12) Linear difference operators (47B39)

Related Items (22)

Asymptotic stability of small bound state of nonlinear quantum walks ⋮ Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators ⋮ Dispersion estimates for one-dimensional discrete Dirac equations ⋮ Properties of the scattering matrix and dispersion estimates for Jacobi operators ⋮ Ground states in spatially discrete non-linear Schrödinger models ⋮ Existence and Asymptotic Stability of Quasi-Periodic Solutions of Discrete NLS with Potential ⋮ Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation ⋮ Dispersion estimates for one-dimensional discrete Schrödinger and wave equations ⋮ Behavior for large time of a two-component chain of harmonic oscillators ⋮ Dispersive properties for discrete Schrödinger equations ⋮ Dispersive estimates for periodic discrete one-dimensional Schrödinger operators ⋮ A discrete Schrödinger operator on a graph ⋮ On spectral problems of discrete Schrödinger operators. ⋮ Large-time behavior of an infinite system of harmonic oscillators on the half-line ⋮ Dispersive estimate for two-periodic discrete one-dimensional Schrödinger operator ⋮ \(L^p\) continuity of wave operators in \(\mathbb Z\) ⋮ Dispersive estimate for quasi-periodic Schrödinger operators on \(1-d\) lattices ⋮ Stabilization of small solutions of discrete NLS with potential having two eigenvalues ⋮ Dispersive estimates for quantum walks on 1D lattice ⋮ Decay and Strichartz Estimates for DNLS ⋮ A complete classification of threshold properties for one-dimensional discrete Schrödinger operators ⋮ Limiting absorption principle for the 1D discrete Dirac equation

Cites Work

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• Dispersive estimates for Schrödinger operators in dimensions one and three
• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Sum rules for Jacobi matrices and their applications to spectral theory
• \(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
• On dispersive properties of discrete 2D Schrödinger and Klein-Gordon equations
• Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
• Dispersive estimates for 1D discrete Schrödinger and Klein–Gordon equations
• Excitation thresholds for nonlinear localized modes on lattices
• Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations

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