Semiclassical form factor for chaotic systems with spin \(\frac 12\). (English) Zbl 0966.81020

Summary: We study the properties of the two-point spectral form factor for classically chaotic systems with spin \({1\over 2}\) 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 formula requires an appropriate variant of the equidistribution principle of long periodic orbits as well as the notion of a skew product of the classical translational and spin dynamics. Provided this skew product is mixing, we show that generically the diagonal approximation of the form factor coincides with the respective predictions from random matrix theory.


81Q50 Quantum chaos
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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