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PreprintCC BY 4.0arXiv

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

  • Mashrab Akramov
  • Carsten Trunk
  • Davron Matrasulov
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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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Cite

BibTeXRIS
BibTeX
@misc{akramov2026discrete,
  title = {{Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice}},
  author = {Mashrab Akramov and Carsten Trunk and Davron Matrasulov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07539},
  eprint = {2609.07539},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07539},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice
AU  - Mashrab Akramov
AU  - Carsten Trunk
AU  - Davron Matrasulov
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07539
UR  - https://arxiv.org/abs/2609.07539
AB  - 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.
ER  -