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The two-point correlation function of chaotic systems with spin 1/2 isevaluated using periodic orbits. The spectral form factor for all times thusbecomes accessible. Equivalence with the predictions of random matrix theoryfor the Gaussian symplectic ensemble is demonstrated. A duality between theunderlying generating functions of the orthogonal and symplectic symmetryclasses is semiclassically established.

Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2