Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 29: Quantum Chaos I

DY 29.4: Talk

Thursday, March 17, 2011, 11:00–11:15, ZEU 255

Transport moments beyond the leading order — Gregory Berkolaiko¹ and •Jack Kuipers² — ¹epartment of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA — ²Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such trajectories we show by using graphical recursions how we can obtain the moments of various transport quantities. In particular we give the moment generating function of the transmission and reflection eigenvalues at the first two subleading orders in the inverse channel number for systems with and without time reversal symmetry. These results suggest patterns which could hold for higher order corrections and which would match the low order moments derived from random matrix results. The techniques can also incorporate an energy dependence which allows us to show that the gap in the density of states of chaotic Andreev billiards is robust against the subleading corrections and to obtain the next orders of the moment generating function of the Wigner delay times. Furthermore, the graphical representation provides an intuitive picture for non-linear statistics and we conclude with some generating functions for the correlation between transport moments.