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

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 $-e^{3}I/105\mathrm{}$ at high voltages and to a positive value ${2e}^{2}T/3R$ at $V=0\mathrm{}$ changing its sign at $\mathrm{eV}\sim 20\hspace{0.5em}\mathrm{T}.$