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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2605.09249 |
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| _version_ | 1866914548716404736 |
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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 |