Time-dependent theory of non-linear response and current fluctuations

TL;DR

This paper develops a comprehensive non-linear response theory for time-dependent quantum systems, deriving generalized formulas for conductance and noise that explain asymmetries and negative excess noise in mesoscopic devices.

Contribution

It introduces a generalized Kubo formula and fluctuation-dissipation relation applicable to arbitrary time-dependent Hamiltonians and complex mesoscopic setups.

Findings

Derived a generalized Kubo formula for non-linear response.

Established current-conserving conductance and noise matrices.

Explained asymmetries and negative excess noise in mesoscopic systems.

Abstract

A general non-linear response theory is derived for an arbitrary time-dependent Hamiltonian, not necessarily obeying time-reversal symmetry. This allows us to obtain a greatly generalized Kubo type formula. Applied to a mesoscopic system with any type of interactions, and coupled to multiple probes and gates with arbitrarily time-dependent voltages, we derive current-conserving differential conductance and current fluctuation matrices obeying a generalized Fluctuation-Dissipation Theorem. This relation provides a common explanation for asymmetries of the excess noise in several non-linear mesoscopic systems, as well as of its surprising negative sign.