| We consider a general Hamiltonian with two degrees of freedom where one of them is canonical and the other a spin. Systems in this category include, for example, those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. The quantum propagator for such systems can be written in a basis formed by the product of a canonical and a spin coherent states. Starting from a path integral representation for the quantum propagator in this mixed basis we derive its semiclassical limit and study some special cases -- separable systems, the limit of very large spins and the case of spin-1/2 (J. Phys. A: Math. Gen. 39, 3085 (2006)). Moreover, with the semiclassical propagator in hand, we also derive a semiclassical level density and compare it with other trace formulas including spin variables found in the literature (J. Math. Phys. 48, 112103 (2007)). Numerical applications are being prepared to be presented at the conference. |
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