Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice

• URL: http://arxiv.org/abs/2609.07539v1
• Date: Mon, 07 Sep 2026 14:21:39 GMT
• Title: Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice
• Abstract summary: We study the one-dimensional time-independent discrete Dirac equation on graphs with discrete edges.<n>This approach offers a systematic framework for analyzing relativistic quantum transport on branched structures relevant to nanostructures and quantum device design.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the one-dimensional time-independent discrete Dirac equation on graphs with discrete edges. Both continuous and discrete formulations of the graphs are considered, with particular focus on star graphs with three edges as a simple example. Exact solutions for eigenstates and spectra are derived and compared with the continuum case, showing good agreement in tabulated results. This approach offers a systematic framework for analyzing relativistic quantum transport on branched structures relevant to nanostructures and quantum device design.

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