Quantum cat maps with spin 1/2

Abstract

We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a two-spinor precessing in a magnetic field. The trace formula is applied to semiclassical correlation densities of the quantum map, which, according to the conjecture of Bohigas, Giannoni and Schmit, are expected to converge to those of the circular symplectic ensemble (CSE) of random matrices. In particular, we show that the diagonal approximation of the spectral form factor for small arguments agrees with the CSE prediction. The results are confirmed by numerical investigations.

26 pages, 3 figures

References in corpus (3)

• Short-range plasma model for intermediate spectral statistics
• Semiclassical form factor for chaotic systems with spin 1/2
• Semiclassical expectation values for relativistic particles with spin 1/2

Cited by in corpus (6)

• Spectral Statistics for the Dirac Operator on Graphs
• Intermediate statistics in quantum maps
• The spin contribution to the form factor of quantum graphs
• GSE statistics without spin
• Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit
• The spectral form factor for quantum graphs