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

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.

6 pages, 5 figures; added references, final version

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• Dynamical model for the quantum-to-classical crossover of shot noise
• Ballistic quantum transport at high energies and high magnetic fields
• Noiseless scattering states in a chaotic cavity
• Shot noise in the chaotic-to-regular crossover regime
• Simulation of Electron Transport through a Quantum Dot with Soft Walls
• Shot noise and transport in small quantum cavities with large openings
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Cited by in corpus (2)

• Diffractive paths for weak localization in quantum billiards
• Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems