Distribution of voltage fluctuations in a current-biased conductor

TL;DR

This paper analyzes voltage fluctuations in a current-driven conductor, revealing the distribution of accumulated phase and its relation to shot noise, with different regimes showing Pascal and chi-square distributions.

Contribution

It introduces the distribution of voltage fluctuations and the phase distribution in a current-biased conductor, highlighting their differences from charge fluctuation distributions.

Findings

Distribution of phase is Pascal (binomial) in single-channel case.

Weak-coupling limit yields a Poissonian phase distribution.

Tunneling limit results in a chi-square phase distribution.

Abstract

We calculate the fluctuating voltage V(t) over a conductor driven out of equilibrium by a current source. This is the dual of the shot noise problem of current fluctuations I(t) in a voltage-biased circuit. In the single-channel case the distribution of the accumulated phase Phi=(e/hbar)\int Vdt is the Pascal (or binomial waiting-time) distribution -- distinct from the binomial distribution of transferred charge Q=\int Idt. The weak-coupling limit of a Poissonian P(Phi) is reached in the limit of a ballistic conductor, while in the tunneling limit P(Phi) has the chi-square form.