Distribution of voltage fluctuations in a current-biased conductor

摘要

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