Semiclassical approach to the ac conductance of chaotic cavities

Abstract

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime.

Fermi liquid approach to the quantumRCcircuit: Renormalization group analysis of the Anderson and Coulomb blockade models

“…The charge relaxation resistance has also been investigated for small metallic islands where the tunnel junction to the reservoir is described by a large number of weakly transmitting channels [53,54]. In this regime, a mapping to the problem of a single particle on a ring subject to dissipation has been exploited [55] to demonstrate a new fixed point at large transparency associated to the quantized resistance R q = h/e 2 .…”

Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions

“…Governing the crossover is the Ehrenfest time, which, when it is small compared to the average time spent inside the cavity, separates the two cases as in Definition 1. For larger Ehrenfest time, when RMT stops being applicable, the semiclassical treatment correspondingly becomes notably more complicated [18,19,30,56,57,68,69,72,73]. However, a particular way of partitioning the diagrams provided enough of a simplification that the contribution of all the leading order diagrams could be obtained [70].…”

Ehrenfest-time dependence of counting statistics for chaotic ballistic systems

“…Equation (43) can be generalized to ac transport considered in Ref. 29 by including in the latter equation the -dependent factors given in (5) and (6). The result in (43) again splits into two parts, with the first involving the semiclassical moments M(n) calculated in Ref.…”

“…This equation incorporates both (27) and (29). If we introduce the notation M[i,j ] ≡ max{t enc,i ,t enc,j }, we can then define the times t i = t i − M[kī,k i+1 ] as before (28).…”