The spin contribution to the form factor of quantum graphs
arXiv:nlin/0304046 · doi:10.1088/0305-4470/36/27/101
Abstract
Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(τ) due to spin propagation around orbits produce higher order terms in the small-τasymptotics in agreement with symplectic random matrix ensembles. We determine conditions on the group of spin rotations sufficient to generate CSE statistics.
9 pages
References in corpus (5)
- Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
- Spectral Statistics for the Dirac Operator on Graphs
- The Leading Off-Diagonal Correction to the Form Factor of Large Graphs
- Semiclassical form factor for chaotic systems with spin 1/2
- Quantum cat maps with spin 1/2
Cited by in corpus (24)
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- No quantum ergodicity for star graphs
- Quantum statistics on graphs
- Transparent Quantum Graphs
- GSE statistics without spin
- Semiclassical approach to discrete symmetries in quantum chaos
- Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction
- The mass of simple and higher-order networks
- Dirac gauge theory for topological spinors in 3+1 dimensional networks
- Semiclassical theory of ballistic transport through chaotic cavities with spin-orbit interaction
- Dirac Particles in Transparent Quantum Graphs: Tunable transport of relativistic quasiparticles in branched structures
- PT-symmetric quantum graphs
- Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs II: semiclassical approach
- An exact trace formula and zeta functions for an infinite quantum graph with a non-standard Weyl asymptotics
- Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
- Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
- Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction
- Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
- Maximal scarring for eigenfunctions of quantum graphs
- Dirac particles on periodic quantum graphs