Universal First-Passage-Time Distribution of Non-Gaussian Currents

TL;DR

This paper studies the distribution of times until a certain amount of charge passes through a conductor, showing a universal approximation that applies to various stochastic processes and confirming a fluctuation relation experimentally.

Contribution

It introduces a universal analytical approximation for first-passage-time distributions in non-Gaussian currents, validated by experiments and numerical calculations.

Findings

Excellent agreement between experiment and theory

High-accuracy analytical approximation for non-Gaussian statistics

Verification of fluctuation relation between positive and negative thresholds

Abstract

We investigate the fluctuations of the time elapsed until the electric charge transferred through a conductor reaches a given threshold value. For this purpose, we measure the distribution of the first-passage times for the net number of electrons transferred between two metallic islands in the Coulomb blockade regime. Our experimental results are in excellent agreement with numerical calculations based on a recent theory describing the exact first-passage-time distributions for any non-equilibrium stationary Markov process. We also derive a simple analytical approximation for the first-passage-time distribution, which takes into account the non-Gaussian statistics of the electron transport, and show that it describes the experimental distributions with high accuracy. This universal approximation describes a wide class of stochastic processes and can be used beyond the context of mesoscopic charge transport. In addition, we verify experimentally a fluctuation relation between the first-passage-time distributions for positive and negative thresholds.