Quantum-to-classical crossover of mesoscopic conductance fluctuations

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 ${\tau }_D\propto M/N$. 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.

5 pages, 5 figures: one figure added, references updated

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Cited by in corpus (26)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization
• A semiclassical theory of the Ehrenfest-time dependence of quantum transport in ballistic quantum dots
• Quantum-to-classical correspondence in open chaotic systems
• Ehrenfest-time dependence of weak localization in open quantum dots
• Semiclassical roots of universality in many-body quantum chaos
• Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
• Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport
• Ehrenfest time in the weak dynamical localization
• Dephasing in quantum chaotic transport: a semiclassical approach
• Semiclassical theory of the Ehrenfest-time dependence of quantum transport
• Quantum-to-Classical Crossover in Full Counting Statistics
• Exponential sensitivity to dephasing of electrical conduction through a quantum dot
• The spectral form factor near the Ehrenfest-time
• Classical limit of transport in quantum kicked maps
• Weak localization of the open kicked rotator
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Semiclassical theory of a quantum pump
• Transport through open quantum dots: making semiclassics quantitative
• Criticality in the Quantum Kicked Rotor with a Smooth Potential
• Universal parametric correlations in the classical limit of quantum transport
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• Semiclassical theory of the interaction correction to the conductance of antidot arrays
• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Semiclassical theory of speckle correlations
• Semiclassical theory of persistent current fluctuations in ballistic chaotic rings