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 nonequilibrium 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.
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| http://dx.doi.org/10.1103/PhysRevLett.122.230602 | DOI Listing |
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Article Synopsis
- This paper investigates a model where a particle diffuses along a line and experiences stochastic resetting at a rate r, while its position may be rescaled by a factor a (positive or negative).
- When |a|<1, the long-term position distribution stabilizes as a symmetric Gaussian shape near the peak at x=0, but decays exponentially for larger |x|.
- The study finds that the mean first-passage time (MFPT) to a target varies with different values of a, with the optimal MFPT indicating that negative rescaling aids in target search, unlike positive rescaling, which makes the search less efficient.
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