Berkolaiko, Gregory and Kuipers, Jack (2011) Transport moments beyond the leading order. NEW JOURNAL OF PHYSICS, 13: 063020. ISSN 1367-2630,
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For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories that enter and exit the system. With a semiclassical treatment involving fine correlations between such trajectories, we develop a diagrammatic technique to calculate the moments of various transport quantities. Namely, we find the moments of the transmission and reflection eigenvalues for systems with and without time-reversal symmetry. We also derive related quantities involving an energy dependence: the moments of the Wigner delay times and the density of states of chaotic Andreev billiards, where we find that the gap in the density persists when subleading corrections are included. Finally, we show how to adapt our techniques to nonlinear statistics by calculating the correlation between transport moments. In each setting, the answer for the nth moment is obtained for arbitrary n (in the form of a moment generating function) and for up to three leading orders in terms of the inverse channel number. Our results suggest patterns that should hold for further corrections, and by matching with the lower-order moments available from random matrix theory, we derive the likely higher-order generating functions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NONLINEAR-SIGMA-MODEL; QUANTUM TRANSPORT; SEMICLASSICAL APPROACH; SPECTRAL STATISTICS; CHAOTIC SCATTERING; DISORDERED METALS; ANDREEV BILLIARDS; MATRIX THEORY; CAVITIES; LOCALIZATION; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Jun 2020 06:39 |
| Last Modified: | 09 Jun 2020 06:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20665 |
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