PT-symmetric quantum graphs
| Autor: | Davron Matrasulov, K. K. Sabirov, J. R. Yusupov |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Pure mathematics FOS: Physical sciences General Physics and Astronomy 01 natural sciences 010305 fluids & plasmas Schrödinger equation symbols.namesake Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences Boundary value problem 010306 general physics Quantum Mathematical Physics Eigenvalues and eigenvectors Physics Quantum Physics Condensed Matter - Mesoscale and Nanoscale Physics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Condensed Matter - Other Condensed Matter Modeling and Simulation Quantum graph symbols Graph (abstract data type) Quantum Physics (quant-ph) Hamiltonian (quantum mechanics) Realization (systems) Other Condensed Matter (cond-mat.other) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 52:155302 |
| ISSN: | 1751-8121 1751-8113 |
| DOI: | 10.1088/1751-8121/ab03f8 |
| Popis: | We consider branched quantum wires, whose connection rules provide PT-symmetry for the Schrodinger equation on graph. For such PT-symmetric quantum graph we derive general boundary conditions which keep the Hamiltonian as PT-symmetric with real eigenvalues and positively defined norm. Explicit boundary conditions which are consistent with the general PT-symmetric boundary conditions are presented. Secular equations for finding the eigenvalues of the quantum graph are derived. Breaking of the Kirchhoff rule at the branching point is shown. Experimental realization of PT-symmetric quantum graphs on branched optical waveguides is discussed. |
| Databáze: | OpenAIRE |
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