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Auteurs principaux: Queiroz, Lucas K. R., Alves, Van Sérgio, Bezerra, Nilberto, Fernández, Luis, Peña, Francisco
Format: Preprint
Publié: 2026
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Accès en ligne:https://arxiv.org/abs/2605.09249
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author Queiroz, Lucas K. R.
Alves, Van Sérgio
Bezerra, Nilberto
Fernández, Luis
Peña, Francisco
author_facet Queiroz, Lucas K. R.
Alves, Van Sérgio
Bezerra, Nilberto
Fernández, Luis
Peña, Francisco
contents We investigate a Dirac-type equation in (2+1) dimensions modified by Lifshitz spatial derivatives with dynamical exponent $z=2$, focusing on the spectral properties of bound states under radial confinement. Analytical solutions are obtained for constant backgrounds, hard-wall confinement, and harmonic potentials, while logarithmic confinement is treated numerically via the Numerov method and complemented by a semiclassical WKB analysis. The resulting spectra exhibit characteristic scaling laws governed by the Lifshitz parameter $b$, including $E - M \propto b/R_0^2$ for hard-wall confinement, $E - M \propto \sqrt{2b}\,ω$ for harmonic trapping, and $E - M \sim α\ln\sqrt{b}$ in the semiclassical regime of logarithmic confinement. These results provide a consistent characterization of how higher-order spatial derivatives modify bound-state spectra in two-dimensional Dirac systems and may be relevant for effective descriptions of materials with quadratic low-energy dispersion, such as bilayer graphene and related anisotropic 2D systems.
format Preprint
id arxiv_https___arxiv_org_abs_2605_09249
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Bound-State Spectra of a Lifshitz-Type Dirac Equation in (2+1) Dimensions
Queiroz, Lucas K. R.
Alves, Van Sérgio
Bezerra, Nilberto
Fernández, Luis
Peña, Francisco
Strongly Correlated Electrons
Quantum Physics
We investigate a Dirac-type equation in (2+1) dimensions modified by Lifshitz spatial derivatives with dynamical exponent $z=2$, focusing on the spectral properties of bound states under radial confinement. Analytical solutions are obtained for constant backgrounds, hard-wall confinement, and harmonic potentials, while logarithmic confinement is treated numerically via the Numerov method and complemented by a semiclassical WKB analysis. The resulting spectra exhibit characteristic scaling laws governed by the Lifshitz parameter $b$, including $E - M \propto b/R_0^2$ for hard-wall confinement, $E - M \propto \sqrt{2b}\,ω$ for harmonic trapping, and $E - M \sim α\ln\sqrt{b}$ in the semiclassical regime of logarithmic confinement. These results provide a consistent characterization of how higher-order spatial derivatives modify bound-state spectra in two-dimensional Dirac systems and may be relevant for effective descriptions of materials with quadratic low-energy dispersion, such as bilayer graphene and related anisotropic 2D systems.
title Bound-State Spectra of a Lifshitz-Type Dirac Equation in (2+1) Dimensions
topic Strongly Correlated Electrons
Quantum Physics
url https://arxiv.org/abs/2605.09249