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
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