Article

PT-symmetric quantum graphs

D. U. MatrasulovTurin Polytechnic University in Tashkent, 17 Niyazov Str., 100095, Tashkent, UzbekistanK K SabirovTashkent University of Information Technology, Amir Temur Avenue 108, Tashkent 100200, UzbekistanJambul YusupovTurin Polytechnic University in Tashkent, 17 Niyazov Str., 100095, Tashkent, Uzbekistan

Journal of Physics A Mathematical and Theoreticaljournal2019en

ABI

Abstract

Abstract We consider PT-symmetric quantum graphs, in which the branching points provide PT-symmetric boundary conditions for the Schrödinger equation on a graph. For such branched quantum wires, we derive general boundary conditions, which keep the Hamiltonian as PT-symmetric with real eigenvalues and positively defined norm of the eigenfunctions. Secular equations for finding the eigenvalues of the quantum graph are derived. Breaking the Kirchhoff rule at the branching points in such systems is shown. Experimental realization of PT-symmetric quantum graphs on branched optical waveguides is discussed.

Topics

Quantum Mechanics and Non-Hermitian Physics Spectral Theory in Mathematical Physics Algebraic and Geometric Analysis

Identifiers

DOI: 10.1088/1751-8121/ab03f8

Citations and references

Cited by 10 46 references

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