Continuum limits for discrete Dirac operators on 2D square lattices

DOI10.1007/s13324-023-00809-7zbMath1530.47056arXiv2109.04052OpenAlexW4376954997MaRDI QIDQ6041377

Tomio Umeda, Karl Michael Schmidt

Publication date: 26 May 2023

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.04052

zbMATH Keywords

complex potentialsspectrumdiscrete Fourier transformdiscrete Dirac operatorscontinuum limitsDirac operators on square lattices

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Operators arising in mathematical physics (47B93)

Related Items

Discrete approximations to Dirac operators and norm resolvent convergence

Cites Work

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• Location of eigenvalues of non-self-adjoint discrete Dirac operators
• Dispersion estimates for one-dimensional discrete Dirac equations
• A remark on the limiting absorption method for Dirac operators
• On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential
• Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators
• GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems
• On a continuum limit of discrete Schrödinger operators on square lattice
• The spectrum of discrete Dirac operator with a general boundary condition
• Discrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices
• One-dimensional discrete Dirac operators in a decaying random potential. I: Spectrum and dynamics
• A value region problem for continued fractions and discrete Dirac equations
• Dynamical localization for discrete Anderson Dirac operators
• Further results in the theory of monodiffric functions
• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions
• Spectrum and scattering function of the impulsive discrete Dirac systems
• Continuum limit for lattice Schrödinger operators
• The cubic eigenparameter dependent discrete Dirac equations with principal functions
• An application of the inverse scattering problem for the discrete Dirac operator
• Spectral theory of first-order systems: From crystals to Dirac operators
• The Discrete Self-Adjoint Dirac Systems of General Type: Explicit Solutions of Direct and Inverse Problems, Asymptotics of Verblunsky-Type Coefficients and the Stability of Solving of the Inverse Problem
• Honeycomb lattice potentials and Dirac points
• On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit