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We perform a comparative study of the quantum and classical transport probabilities of low-energy quasiparticles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on the dependence of the transport on the strength of an applied magnetic field $B$. With increasing field strength the classical dynamics changes from mixed to regular phase space. Averaging out the quantum fluctuations, we find an excellent agreement between the quantum and classical transport coefficients in the complete range of field strengths. This allows an overall description of the non-monotonic behavior of the average magnetoconductance in terms of the corresponding classical trajectories, thus, establishing a basic tool useful in the design and analysis of experiments.
We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the limitations of
We demonstrate that the exact quantum mechanical calculations are in good agreement with the semiclassical predictions for rectangular Andreev billiards and therefore for a large number of open channels it is sufficient to investigate the Bohr-Sommer
We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cut-off in the path length distribution $P(s)$ will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculat
Comparing the results of exact quantum calculations and those obtained from the EBK-like quantization scheme of Silvestrov et al [Phys. Rev. Lett. 90, 116801 (2003)] we show that the spectrum of Andreev billiards of mixed phase space can basically be
We study the transport properties of low-energy (quasi)particles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We consider four different geometrical setups and focus on the dependence of trans