Noiseless scattering states in a chaotic cavity

Abstract

Shot noise in a chaotic cavity (Lyapunov exponent $\lambda$, level spacing $\delta$, linear dimension $L$), coupled by two $N$-mode point contacts to electron reservoirs, is studied as a measure of the crossover from stochastic quantum transport to deterministic classical transport. The transition proceeds through the formation of {\em fully} transmitted or reflected scattering states, which we construct explicitly. The fully transmitted states contribute to the mean current $\bar{I}$, but not to the shot-noise power $S$. We find that these noiseless transmission channels do not exist for $N\alt\sqrt{k_{F}L}$, where we expect the random-matrix result $S/2e\bar{I}=1/4$. For $N\agt\sqrt{k_{F}L}$ we predict a suppression of the noise $\propto (k_{F}L/N^2{)}^{N\delta /\pi \hslash \lambda }$. This nonlinear contact dependence of the noise could help to distinguish ballistic chaotic scattering from random impurity scattering in quantum transport.

4 pages, 4 figures

References in corpus (2)

• Adiabatic quantization of Andreev levels
• Shot noise and transport in small quantum cavities with large openings

Cited by in corpus (15)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Ehrenfest time dependent suppression of weak localization
• Quantum-to-classical correspondence in open chaotic systems
• Andreev billiards
• Ehrenfest-time dependence of weak localization in open quantum dots
• Polarized Electric Current in Semiclassical Transport with Spin-Orbit Interaction
• Shot noise in the chaotic-to-regular crossover regime
• Quantum-to-classical crossover of mesoscopic conductance fluctuations
• Simulation of Electron Transport through a Quantum Dot with Soft Walls
• Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport
• Exponential sensitivity to dephasing of electrical conduction through a quantum dot
• 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
• Pseudo-Path Semiclassical Approximation to Transport through Open Quantum Billiards: Dyson Equation for Diffractive Scattering