The Interacting Mesoscopic Capacitor Out of Equilibrium

Abstract

We consider the full nonequilibrium response of a mesoscopic capacitor in the large transparency limit, exactly solving a model with electron-electron interactions appropriate for a cavity in the quantum Hall regime. For a cavity coupled to the electron reservoir via an ideal point contact, we show that the response to any time-dependent gate voltage $V_{\mathrm{g}}(t)$ is strictly linear in $V_{\mathrm{g}}$. We analyze the charge and current response to a sudden gate voltage shift, and find that this response is not captured by a simple circuit analogy. In particular, in the limit of strong interactions a sudden change in the gate voltage leads to the emission of a sequence of multiple charge pulses, the width and separation of which are controlled by the charge-relaxation time ${\tau }_{\mathrm{c}}=h{C}_{\mathrm{g}}/e^2$ and the time of flight ${\tau }_{\mathrm{f}}$. We also consider the effect of a finite reflection amplitude in the point contact, which leads to nonlinear-in-gate-voltage corrections to the charge and current response.

14 pages, 11 figures

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• Influence of channel mixing in fermionic Hong-Ou-Mandel experiments
• Phase-Coherent Dynamics of Quantum Devices With Local Interactions
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• Anomalous Joule law in the adiabatic dynamics of a normal-superconductor quantum dot
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• Spin-charge separation in an Aharonov-Bohm interferometer
• Nonlocal Transport of Heat in Equilibrium Drift-Diffusion Systems
• Quantum transport phenomena induced by time-dependent fields