PubMed Health⌕ Search

Biomedical subjects

Z Kaufmann

Publications and source records attributed to Z Kaufmann.

7 recordsLinked to original sources
PubMed2006

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.

Journal Article↗
PubMed2002

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. We show that the energy gap, in units of Thouless energy, may exceed the value predicted earlier from random matrix theory for chaotic billiards.

Journal Article↗
PubMed2001

Comparison of averages of flows and maps.

It is shown that in transient chaos there is no direct relation between averages in a continuous time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincaré map. In contrast to permanent chaos, results obtained from the Poincaré map can even be qualitatively incorrect. The reason is that the return time between intersections on the Poincaré surface becomes relevant. However, after introducing a true-time Poincaré map, quantities known from the usual Poincaré map, such as conditionally invariant measure and natural measure, can be generalized to this case. Escape rates and averages, e.g., Liapunov exponents and drifts, can be determined correctly using these measures. Significant differences become evident when we compare with results obtained from the usual Poincaré map.

Journal Article↗
PubMed1999

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. The result makes it possible to generalize the Gaspard-Nicolis formula [Phys. Rev. Lett. 65, 1693 (1990)] to this transient case in deterministic systems.

Journal Article↗