Quantum-to-classical crossover of mesoscopic conductance fluctuations

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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 ∝ M² at fixed mean dwell time τD ∝ M/N. The universal quantum fluctuations dominate over the nonuniversal classical fluctuations if N < √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.