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Quantum-to-classical crossover of mesoscopic conductance fluctuations

J. Tworzydlo·A. Tajic·C. W. J. Beenakker
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Abstract

We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to electron reservoirs. Both a fully quantum mechanical and a semiclassical calculation are presented, and found to be in good agreement. The mean squared conductance fluctuations reach the universal quantum limit of random-matrix-theory for small systems. For large systems they increase $\propto M^2$ at fixed mean dwell time $τ_D \propto M/N$. The universal quantum fluctuations dominate over the nonuniversal classical fluctuations if $N < \sqrt{M}$. When expressed as a ratio of time scales, the quantum-to-classical crossover is governed by the ratio of Ehrenfest time and ergodic time.

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J. Tworzydlo, A. Tajic, C. W. J. Beenakker. 2004-01-15. Quantum-to-classical crossover of mesoscopic conductance fluctuations. https://doi.org/10.1103/physrevb.69.165318

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