Multiple solutions for a self-consistent Dirac equation in two dimensions

DOI10.1063/1.5005998zbMath1393.81013arXiv1709.06387OpenAlexW2754174163MaRDI QIDQ4639351

William Borrelli

Publication date: 9 May 2018

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

Full work available at URL: https://arxiv.org/abs/1709.06387

zbMATH Keywords

nonlinear Schrödinger equationfountain theoremelectron transportDirichlet Laplacianvariational argumentRiesz operatorDirac materialsinfinite mass boundary conditionCauchy operator in a bounded \(R^2\) domain (spectral definition)effective massless Dirac equationgraphene samplesemiclassical (WKB) limit

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Spectrum, resolvent (47A10) NLS equations (nonlinear Schrödinger equations) (35Q55) Boundary value problems for PDEs with pseudodifferential operators (35S15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Transport processes in time-dependent statistical mechanics (82C70) Statistical mechanics of nanostructures and nanoparticles (82D80) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39) Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators (35L86)

Related Items (7)

Resolvent convergence to Dirac operators on planar domains ⋮ Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations ⋮ Unnamed Item ⋮ On the nonlinear Dirac equation on noncompact metric graphs ⋮ Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit ⋮ Weakly localized states for nonlinear Dirac equations ⋮ An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity

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