Statistics of Transmission Eigenvalues in Two-Dimensional Quantum Cavities: Ballistic versus Stochastic Scattering

TL;DR

This paper studies the statistical distribution of transmission eigenvalues in two-dimensional quantum dots, revealing different quantum-to-classical crossover behaviors in clean versus disordered cavities through ab-initio simulations.

Contribution

It introduces a hybrid crossover model combining ballistic and stochastic limits to better describe transmission eigenvalue distributions in disordered quantum cavities.

Findings

Noiseless scattering states emerge in clean cavities.

Crossover behavior is insensitive to cavity chaoticity but sensitive to disorder.

Hybrid model effectively captures intermediate scattering regimes.

Abstract

We investigate the statistical distribution of transmission eigenvalues in phase-coherent transport through quantum dots. In two-dimensional ab-initio simulations for both clean and disordered two-dimensional cavities, we find markedly different quantum-to-classical crossover scenarios for these two cases. In particular, we observe the emergence of ``noiseless scattering states'' in clean cavities, irrespective of sharp-edged entrance and exit lead mouths. We find the onset of these ''classical'' states to be largely independent of the cavity's classical chaoticity, but very sensitive with respect to bulk disorder. Our results suggest that for weakly disordered cavities the transmission eigenvalue distribution is determined both by scattering at the disorder potential and the cavity walls. To properly account for this intermediate parameter regime we introduce a hybrid crossover scheme which combines previous models that are valid in the ballisic and the stochastic limit, respectively.