Quantum graphs with spin Hamiltonians

TL;DR

This paper reviews quantization methods for metric graphs incorporating spin, focusing on Dirac, Pauli, and Rashba Hamiltonians, and compares their spectral and localization properties.

Contribution

It introduces and compares three spin Hamiltonian operators for quantum graphs, expanding the theoretical framework beyond traditional spin-zero models.

Findings

Analysis of trace formulas for spin Hamiltonians

Comparison of spectral statistics across different models

Insights into spin-orbit localization phenomena

Abstract

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.