Quantum shot noise: Expansions in powers of the pulse density

Abstract

Quantum shot noise consists of individual pulses which contribute time-dependent (operator) “potentials” toward a total potentialV(t). The averaged quantity 〈T exp ∫ ^t _t0 dt′V(t′)〉 in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse densityυ. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening.