2000/12/07 by Stefan Keppeler, Jens Marklof, Francesco Mezzadri
Chemistry · Mathematics · Physics and Astronomy · #Conjecture #Diagonal #Field (mathematics) #Geometry #Mathematical Dynamics and Fractals #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Physics #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Semiclassical physics #Spin (aerodynamics) #Spinor #Symplectic geometry #TRACE (psycholinguistics) #Torus #nlin.CD
paper · pdf · doi:10.1088/0951-7715/14/4/304
published as Nonlinearity 14 (2001) 719-738 · 26 pages, 3 figures
arxiv created 2000/12/07 · openalex publication_date 2001/05/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive a semiclassical trace formula for quantized chaotic transformations of the torus coupled to a 2-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.