Quantum cat maps with spin 1/2

Details Quantum cat maps with spin 1/2 Quantum cat maps with spin 1/2

2000-12-07

arxiv.org/abs/nlin/0012012v1

Nonlinearity 14 (2001) 719-738

Nonlinear Sciences

Chaotic Dynamics

26 pages, 3 figures

Scientific paper

10.1088/0951-7715/14/4/304

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.

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