Quantum graphs with spin Hamiltonians

Details Quantum graphs with spin Hamiltonians Quantum graphs with spin Hamiltonians

2007-12-06

arxiv.org/abs/0712.0869v2

P Exner, JP Keating, P Kuchment, T Sunada, A Teplyaev (Eds) Analysis on graphs and its applications, Proceedings of Symposia i

Physics

Mathematical Physics

17 pages, typos corrected, references and comments added

Scientific paper

The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many applications, for example modeling an electron (which has spin-1/2) on a network of thin wires, it is necessary to consider operators which allow spin-orbit interaction. The article presents a review of quantization schemes for graphs with three such Hamiltonian operators, the Dirac, Pauli and Rashba Hamiltonians. Comparing results for the trace formula, spectral statistics and spin-orbit localization on quantum graphs with spin Hamiltonians.

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