Fluctuating phase rigidity for a quantum chaotic system with partially broken time-reversal symmetry

The functional {rho}={vert_bar}{integral}d{rvec r}{psi}{sup 2}{vert_bar}{sup 2} measures the phase rigidity of a chaotic wave function {psi}({rvec r}) in the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking time-reversal symmetry, {rho} crosses over from one to zero. We compute the distribution of {rho} in the crossover regime and find that it has large fluctuations around the ensemble average. These fluctuations imply long-range spatial correlations in {psi} and non-Gaussian perturbations of eigenvalues, in precise agreement with results by Fal{close_quote}ko and Efetov [Phys. Rev. Lett. {bold 77}, 912 (1996)] and by Taniguchi {ital et al.} [Europhys. Lett. {bold 27}, 335 (1994)]. As a third implication of the phase-rigidity fluctuations we find correlations in the response of an eigenvalue to independent perturbations of the system. {copyright} {ital 1997} {ital The American Physical Society}