Scattering matrix ensemble for time-dependent transport through a chaotic quantum dot

Abstract

Random matrix theory can be used to describe the transport properties of a chaotic quantum dot coupled to leads. In such a description, two approaches have been taken in the literature, considering either the Hamiltonian of the dot or its scattering matrix as the fundamental random quantity of the theory. In this paper, we calculate the first four moments of the distribution of the scattering matrix of a chaotic quantum dot with a time-dependent potential, thus establishing the foundations of a "random scattering matrix approach" for time-dependent scattering. We consider the limit that the number of channels N coupling the quantum dot the reservoirs is large. In that limit, the scattering matrix distribution is almost Gaussian, with small non-Gaussian corrections. Our results reproduce and unify results for conductance and pumped current previously obtained in the Hamiltonian approach. We also discuss an application to current noise.

Shot noise of photon-excited electron-hole pairs in open quantum dots

“…However, for N ≫ 1 the value of the ensemble averaged correlations S λµ is representative 24 (the average is carried following Refs. [25,26]). We note that to leading order in N ≫ 1 the averaged noise is unaffected by a time-reversal symmetry breaking magnetic field.…”

Photovoltaic Current Response of Mesoscopic Conductors to Quantized Cavity Modes

“…In the classical description of EM fields only the first contribution is found and the second contribution due to electronhole pairs is missed. As noted, in this case the PV current never vanishes simultaneously for all realizations and its RMS value is a monotonic function of the power of the EM radiation [5,6,11,17]. The non-monotonic behavior of the RMS value of the PV current is an indication of the quantum behavior of the EM fields.…”

“…This effect arises in mesoscopic conductors because the phase-coherent transmission through the device almost always violates parity symmetry and the nonequilibrium distribution created by the EM field sets up a steady-state current dictated by this parity violation. When the parity violation is due to random interference, the sign of this current will fluctuate from sample to sample and its rootmean-square (RMS) size in this case depends on the power in the EM field [5,6,8,9,10,11]. Hence after this PV current is calibrated it can be used for detection of the power in the incident EM field.…”

“…When the parity violation is due to random interference, the sign of this current will fluctuate from sample to sample and its rootmean-square (RMS) size in this case depends on the power in the EM field [5,6,8,9,10,11]. Hence after this PV current is calibrated it can be used for detection of the power in the incident EM field.The previous theoretical description [5,6,9,10,11,12] of the PV current has employed a classical treatment of the EM fields, since this description was sufficient for the systems studied experimentally [7,8,13,14,15]. In this case the RMS PV current is a monotonically increasing function of the EM field power.…”

“…The previous theoretical description [5,6,9,10,11,12] of the PV current has employed a classical treatment of the EM fields, since this description was sufficient for the systems studied experimentally [7,8,13,14,15]. In this case the RMS PV current is a monotonically increasing function of the EM field power.…”