Statistics of Transport Properties in Asymmetric Coupled Chaotic Quantum Dots in Series

We investigate transport statistics in a system of two quantum chaotic dots connected by a junction and attached to reservoirs with asymmetric leads. Our results show that as junction width increases, acting as a symmetry-breaking parameter, the scattering-matrix dynamics exhibits a crossover from 2-CUE to 1-CUE. Such crossover had previously been studied for the case of coupled cavities connected to reservoirs with symmetric leads. Analogous symmetry-breaking phenomena is analyzed using Dyson's Brownian motion model, describing matrix diffusion dynamics. The crossover dynamics is explored by gradually widening the junction over time, showing that as the junction expands, the two dots lose their distinct identities leading to a transition in eigenvalue dynamics from non-equilibrium to equilibrium state, governed by the Fokker-Planck equation. We derive exact analytical expressions for the time-dependent average and variance of conductance and shot-noise power. Our analytical results are validated using a random matrix model and tight-binding simulations using KWANT.