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

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...

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Bibliographic Details
Published in:arXiv.org 2007-03
Main Authors: Rotter, Stefan, Aigner, Florian, Burgdörfer, Joachim
Format: Article
Language:English
Subjects:
Computer simulation
Crossovers
Eigenvalues
Entrances
Holes
Quantum dots
Scattering
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0701153