Universal parametric correlations in the classical limit of quantum transport

Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi energy or an applied magnetic field. Here we consider such parameter dependence of quantum transport in a ballistic chaotic cavity in the semiclassical limit obtained by sending $\hslash \to 0$ without changing the classical dynamics of the open cavity. In this limit quantum corrections are shown to have a universal parametric dependence which is not described by random matrix theory.

Figure 1

(Color online) Schematic drawing of quadruples of trajectories that contribute to the conductance autocorrelation function. The true trajectories are piecewise straight, with specular reflection at the boundaries.

Figure 2

Ratio of mean-square pumped current in the true semiclassical limit ${⟨I^2⟩}_{\text{class}}$ and the RMT prediction ${⟨I^2⟩}_{\mathrm{RMT}}$. Inset: Pumping contour in the $(x_1,x_2)$ plane. The ratio shown in the main figure is calculated for a circular pumping contour with radius $x$.