Effective description of the gap fluctuation for chaotic Andreev billiards.

Kormanyos, A. and Kaufmann, Z. and Lambert, C. J. and Cserti, J. (2004) Effective description of the gap fluctuation for chaotic Andreev billiards. Physical review B, 70 (5). 052512.1-052512.4. ISSN 1098-0121

Abstract

We present a numerical study of the universal gap fluctuations and the ensemble averaged density of states (DOS) of chaotic two-dimensional Andreev billiards for finite Ehrenfest time τE . We show that the distribution function of the gap fluctuation for small enough Ehrenfest time can be related to that derived earlier for zero Ehrenfest time. An effective description based on the random matrix theory is proposed giving a good agreement with the numerical results. A systematic linear decrease of the mean field gap with increasing Ehrenfest time τE is observed but its derivative with respect to τE is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is interpreted semiclassically.