AC-condutance of a quantum chaotic cavity (semiclassical approach)

Due to the progress made in the control and the manipulation of mesoscopic structures driven by high frequency periodic voltages, the ac regime has been recently experimentally investigated [1] and consequently its theoretical interest has been renewed. We consider here, a quantum chaotic cavity that is coupled via tunnel barriers and gates to a macroscopic circuit which contains ac-sources [2]. By extending to the ac-transport, the recent trajectory-based semiclassical theory of quantum chaotic transport in presence of tunnel barrier [3], we derive for arbitrary tunneling rates and arbitrary positive Ehrenfest time, the averaged and the weak-localization correction to the screened conductance. Then we use these results to investigate the effect of dephasing on the relaxation resistance of a chaotic capacitor in the linear low frequency regime. This last investigation are in principle relevant to the recent measure of the admittance at zero magnetic flux of a mesoscopic capacitor [1,4].\\ {\bf References}\\ \newcommand\itm[2]{\parbox[t]{1cm}{#1}\parbox[t]{14cm}{#2}} \itm{[1]} {J. Gabelli et al., Science {\bf 313}, 499 (2006).}\\ \itm{[2]} {C. Petitjean et al, {\it in preparation } (2008).}\\ \itm{[3]} {R.S.~Whitney, Phys. Rev. {\bf B, 75}, 235404 (2007).}\\ \itm{[4]} {S.~Nigg and M.~B\"uttiker, Phys. Rev. {\bf B 77}, 085312 (2008).}