发表机构
National University of Uzbekistan; TU Ilmenau; Turin Polytechnic University in Tashkent（乌兹别克斯坦国立大学; 伊尔梅瑙工业大学; 塔什干都灵理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子图上的离散狄拉克方程模型，通过星图示例推导精确解并与连续情形对比，为分支结构中的相对论量子输运提供系统框架。
AI 中文摘要
我们研究了具有离散边的图上的二维时间无关离散狄拉克方程。同时考虑了图的连续和离散表述，特别关注具有三条边的星图作为简单示例。推导了本征态和谱的精确解，并与连续情形进行了比较，表格结果显示两者吻合良好。该方法为分析分支结构上的相对论量子输运提供了一个系统框架，该框架与纳米结构和量子器件设计相关。
英文摘要
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.
Comments15 pages, 1 figure
