# Short time dynamics of molecular junctions after projective measurement

## TL;DR

This paper investigates the immediate effects of projective measurement on the short-time dynamics of a molecular junction modeled by Anderson-Holstein, revealing measurement-induced perturbations and universal scaling behaviors in charge transfer statistics.

## Contribution

It introduces a full-counting statistics approach using Green's functions to analyze the impact of projective measurements on short-time quantum transport in molecular junctions.

## Key findings

- Current is perturbed immediately after measurement.
- Universal scaling observed for high-order cumulants with zero QD occupation.
- Electron-phonon interactions significantly influence short-time current and noise.

## Abstract

In this work, we study the short time dynamics of a molecular junction described by Anderson-Holstein model using full-counting statistics after projective measurement. The coupling between the central quantum dot (QD) and two leads was turned on at remote past and the system is evolved to steady state at time $t=0$, when we perform the projective measurement in one of the lead. Generating function for the charge transfer is expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. It is found that the current is not constant at short times indicating that the measurement does perturb the system. We numerically compare the current behaviors after the projective measurement with those in the transient regime where the subsystems are connected at $t=0$. The universal scaling for high-order cumulants is observed for the case with zero QD occupation due to the unidirectional transport at short times. The influences of electron-phonon interaction on short time dynamics of electric current, shot noise and differential conductance are analyzed.