Dirac particles in transparent quantum graphs: Tunable transport of relativistic quasiparticles in branched structures
Jambul YusupovTurin Polytechnic University in Tashkent, 17 Niyazov Street, 100095, Tashkent, UzbekistanK.K. SabirovTashkent University of Information Technologies, 108 Amir Temur Street, 100200, Tashkent UzbekistanQ. U. AsadovTashkent University of Information Technologies, 108 Amir Temur Street, 100200, Tashkent UzbekistanMatthias EhrhardtBergische Universität Wuppertal, Gaußstrasse 20, D-42119 Wuppertal, GermanyD. U. MatrasulovTurin Polytechnic University in Tashkent, 17 Niyazov Street, 100095, Tashkent, Uzbekistan
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Abstract
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the Dirac equation on metric graphs. Within such an approach, we derive simple constraints, which turn the usual Kirchhoff-type boundary conditions at the vertex equivalent to the transparent ones. Our method is applied to quantum star graph. An extension to more complicated graph topologies is straightforward.
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