Issue |
EPL
Volume 109, Number 5, March 2015
|
|
---|---|---|
Article Number | 50004 | |
Number of page(s) | 6 | |
Section | General | |
DOI | https://doi.org/10.1209/0295-5075/109/50004 | |
Published online | 13 March 2015 |
Capacitance and charge relaxation resistance of chaotic cavities —Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
1 École Normale Supérieure de Cachan - 94235 Cachan cedex, France
2 Univ. Paris Sud; CNRS; Laboratoire de Physique Théorique et Modèles Statistiques, UMR 8626 91405 Orsay cedex, France
(a) aurelien.grabsch@ens-cachan.fr
(b) christophe.texier@u-psud.fr
Received: 11 December 2014
Accepted: 24 February 2015
We consider the AC transport in a quantum RC circuit made of a coherent chaotic cavity with a top gate. Within a random matrix approach, we study the joint distribution for the mesoscopic capacitance and the charge relaxation resistance Rq, where C is the geometric capacitance and Cq the quantum capacitance. We study the limit of a large number of conducting channels N with a Coulomb gas method. We obtain
and show that the relative fluctuations are of order 1/N both for Cq and Rq, with strong correlations
. The detailed analysis of large deviations involves a second-order phase transition in the Coulomb gas. The two-dimensional phase diagram is obtained.
PACS: 05.60.Gg – Quantum transport / 05.45.Mt – Quantum chaos; semiclassical methods / 02.10.Yn – Matrix theory
© EPLA, 2015
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