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We semiclassically derive the leading off-diagonal correction to the spectralform factor of quantum systems with a chaotic classical counterpart. To thisend we present a phase space generalization of a recent approach for uniformlyhyperbolic systems (M. Sieber and K. Richter, Phys. Scr. T90, 128 (2001); M.Sieber, J. Phys. A: Math. Gen. 35, L613 (2002)). Our results coincide withcorresponding random matrix predictions. Furthermore, we study the transitionfrom the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 8 pages, 2 figures; J. Phys. A: Math. Gen. (accepted for publication

Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems