Non-equilibrium noise in a mesoscopic conductor: microscopic analysis

TL;DR

This paper analyzes current fluctuations in mesoscopic conductors under non-equilibrium conditions using the Keldysh technique, deriving general expressions for noise with time-dependent voltages and exploring specific limits like pulses and DC voltages.

Contribution

It provides a microscopic derivation of current noise expressions under non-equilibrium, including phase-sensitive fluctuations and shot noise reduction, extending previous theoretical understanding.

Findings

Derived a general expression for current fluctuations with time-dependent voltage.

Identified phase-sensitive fluctuations with a period related to h/e in voltage pulses.

Confirmed the shot noise reduction factor of 1/3 in the DC limit.

Abstract

Current fluctuations are studied in a mesoscopic conductor using non-equilibrium Keldysh technique. We derive a general expression for the fluctuations in the presence of a time dependent voltage, valid for arbitrary relation between voltage and temperature. Two limits are then treated: a pulse of voltage and a DC voltage. A pulse of voltage causes phase sensitive current fluctuations for which we derive microscopically an expression periodic in $\int V(t)dt$ with the period $h/e$. Applied to current fluctuations in Josephson circuits caused by phase slips, it gives an anomalous contribution to the noise with a logarithmic singularity near the critical current. In the DC case, we get quantum to classical shot noise reduction factor 1/3, in agreement with recent results of Beenakker and B\"uttiker.