Cascade Boltzmann-Langevin approach to higher-order current correlations in diffusive metal contacts

Abstract

The Boltzmann-Langevin approach is extended to calculations of third and fourth cumulants of current in diffusive-metal contacts. These cumulants result from indirect correlations between current fluctuations, which may be considered as ``noise of noise.'' The calculated third cumulant coincides exactly with its quantum-mechanical value. The fourth cumulant tends to its quantum-mechanical value $\ensuremath{-}{e}^{3}I/105$ at high voltages and to a positive value ${2e}^{2}T/3R$ at $V=0$ changing its sign at $\mathrm{eV}\ensuremath{\sim}20 \mathrm{T}.$