Quantum-classical correspondence in the wave functions of andreev billiards.

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that the nonexact velocity reversal and the diffraction at the edges of the normal-superconductor contact render the classical dynamics of these systems mixed indicating the limitations of a widely used retracing approximation. We point out the close relation between the mixed classical phase space and the properties of the quantum states of Andreev billiards, including periodic orbit scarring and localization of the wave function onto other classical phase space objects such as intermittent regions and quantized tori.

Proximity-induced subgaps in andreev billiards.

We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cutoff in the path length distribution P(s) will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculation for different Andreev billiards gives good agreement with the semiclassical predictions when the energy dependent phase shift for Andreev reflections is properly taken into account. Based on this new semiclassical Bohr-Sommerfeld approximation of the density of states, we derive a simple formula for the energy gap.

Relationships among coefficients in deterministic and stochastic transient diffusion.

Systems are studied in which transport is possible due to large extensions with open boundaries in certain directions, but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction or by adsorption. The connection of the total escape rate, the rate of the disappearance, and the diffusion coefficient is investigated. It leads to the observation that the diffusion coefficient defined by is in general different from the one present in the effective Fokker-Planck equation.