Semiclassical Approach to Parametric Spectral Correlation with Spin 1 / 2

Parametric Spectral Correlation with Spin 1/2

Quantum Cat Maps with Spin 1/2

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...

ar X iv : 0 70 8 . 23 75 v 1 [ nl in . C D ] 1 7 A ug 2 00 7 Resummation and the semiclassical theory of spectral statistics

We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation formalism that explicitly preserves the unitarity of the quantum time evolution by incorporating duality relations between short and long classical orbits. ...

Semiclassical form factor for chaotic systems with spin 1 / 2

We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a regularized form factor and discuss the limit in which the so-called diagonal approximation can be recovered. The incorporation of the spin contribution to the trace f...

Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit

We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i. e. it does not follow random matrix theory (RMT). By coupling the map to a spin 1/2, which corresponds to changing the quantisation without altering the classical limit of the dynamics on the torus, we numerically observe a transition...