Brownian-motion model of parametric correlations in ballistic cavities

A Brownian-motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. For systems with unitary symmetry, we find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. For systems with orthogonal, unitary, and symplectic symmetries a formula for the power spectrum of the fluctuations of transport observables as a response to an external adiabatic perturbation is derived. Our formula correctly recovers the Lorentzian-squared behavior obtained, for unitary systems, from semiclassical approaches for the correlation function of conductance fluctuations. {} 1996 The American Physical Society.