Scattering matrix ensemble for time-dependent transport through a chaotic quantum dot
arXiv:cond-mat/0208408 · doi:10.1088/0305-4470/36/12/321
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 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.
26 pages, 6 figures, minor changes
References in corpus (12)
- The Statistical Theory of Quantum Dots
- Quantum Effects in Coulomb Blockade
- Dissipation and noise in adiabatic quantum pumps
- Counting statistics for arbitrary cycles in quantum pumps
- Weak localization and conductance fluctuations of a chaotic quantum dot with tunable spin-orbit coupling
- Noise through Quantum Pumps
- Limits of the dynamical approach to non-linear response of mesoscopic systems
- Full counting statistics of a charge pump in the Coulomb blockade regime
- Charge Screening Effect in Metallic Carbon Nanotubes
- Conductance Fluctuations of Open Quantum Dots under Microwave Radiation
- Time-reversal symmetry breaking by ac field: Effect of commensurability in the frequency domain
- On the semiclassical theory for universal transmission fluctuations in chaotic systems: the importance of unitarity
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