Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
arXiv:cond-mat/0606384 · doi:10.1103/PhysRevB.74.085313
Abstract
The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively. According to the `effective random matrix theory' of Silvestrov, Goorden, and Beenakker [Phys. Rev. Lett. 90, 116801 (2003)], statistical averages involving the quantum-mechanical scattering matrix are given by random matrix theory. While this effective random matrix theory is known not to be applicable for quantum interference corrections to transport, which appear to subleading order in the number of scattering channels N, it is believed to correctly describe quantum transport to leading order in N. We here partially verify this belief, by comparing the predictions of the effective random matrix theory for the ensemble averages of polynomial functions of S and S^dagger of degree 2, 4, and 6 to a semiclassical calculation.
arXiv comment18 pages, 9 figures
References in corpus (34)
- Shot Noise in Mesoscopic Conductors
- Random-Matrix Theory of Quantum Transport
- Semiclassical Foundation of Universality in Quantum Chaos
- Weak-Localization and Integrability in Ballistic Cavities
- Divergence of the Classical trajectories and Weak Localization
- Semiclassical Theory of Chaotic Quantum Transport
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Semiclassical Theory of Chaotic Conductors
- Shot noise in chaotic systems: "classical" to quantum crossover
- Shot noise in semiclassical chaotic cavities
- Nonequilibrium theory of Coulomb blockade in open quantum dots
- 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
- Ehrenfest time dependent suppression of weak localization
- Quantum-to-classical correspondence in open chaotic systems
- Quantum Disorder and Quantum Chaos in Andreev Billiards
- Dynamical model for the quantum-to-classical crossover of shot noise
- Andreev billiards
- Role of divergence of classical trajectories in quantum chaos
- Noiseless scattering states in a chaotic cavity
- Ehrenfest-time dependence of weak localization in open quantum dots
- Scattering matrix ensemble for time-dependent transport through a chaotic quantum dot
- Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems
- Spectral form factor of hyperbolic systems: leading off-diagonal approximation
- Adiabatic quantization of Andreev levels
- Ehrenfest time and the coherent backscattering off ballistic cavities
- Shot noise from action correlations
- Quantum-to-classical crossover of mesoscopic conductance fluctuations
- Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport
- Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard
- The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
- Exponential sensitivity to dephasing of electrical conduction through a quantum dot
- Quantum-to-classical crossover for Andreev billiards in a magnetic field
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- Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
- Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
- Semiclassical gaps in the density of states of chaotic Andreev billiards
- Lifetime statistics in chaotic dielectric microresonators
- Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
- Ehrenfest-time dependence of counting statistics for chaotic ballistic systems
- The density of states of chaotic Andreev billiards
- Semiclassical theory of the Ehrenfest-time dependence of quantum transport
- Conductance fluctuations in chaotic systems with tunnel barriers
- Semiclassics for chaotic systems with tunnel barriers
- Transport moments and Andreev billiards with tunnel barriers
- Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
- The spectral form factor near the Ehrenfest-time
- Anderson localization from classical trajectories
- Ehrenfest time dependence of quantum transport corrections and spectral statistics
- Controlling the Sign of Magnetoconductance in Andreev Quantum Dots
- Semiclassical wavefunctions for open quantum billiards
- Transport through open quantum dots: making semiclassics quantitative
- Semiclassical theory of a quantum pump
- Magnetic-field symmetries of mesoscopic nonlinear conductance
- Semiclassical theory of the interaction correction to the conductance of antidot arrays
- Semiclassical theory of speckle correlations
- Thermoelectric coefficients and the figure of merit for large open quantum dots