Quantum graphs with vertices of a preferred orientation. (English) Zbl 1387.81223
Summary: Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the corresponding band spectra of lattices with square and hexagonal elementary cells showing that they depend heavily on the network topology, in particular, on the degrees of the vertices involved.
MSC:
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
Keywords:
quantum graph; vertex coupling; preferred orientation; square lattice; hexagonal lattice; band spectrumReferences:
| [1] | Berkolaiko, G.; Kuchment, P., Introduction to Quantum Graphs (2013), Amer. Math. Soc.: Amer. Math. Soc. Providence, R.I. · Zbl 1318.81005 |
| [2] | Exner, P., Lattice Kronig-Penney models, Phys. Rev. Lett., 74, 3503-3506 (1995) |
| [3] | Gorbachuk, V. I.; Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations (1991), Kluwer: Kluwer Dordrecht · Zbl 0751.47025 |
| [4] | Harmer, M., Hermitian symplectic geometry and extension theory, J. Phys. A, Math. Gen., 33, 9193-9203 (2000) · Zbl 0983.53051 |
| [5] | Kostrykin, V.; Schrader, R., Kirchhoff’s rule for quantum wires, J. Phys. A, Math. Gen., 32, 595-630 (1999) · Zbl 0928.34066 |
| [6] | Středa, P.; Kučera, J., Orbital momentum and topological phase transformation, Phys. Rev. B, 92, Article 235152 pp. (2015) |
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