Signatures of critical full counting statistics in a quantum-dot chain

TL;DR

This paper investigates how the full counting statistics of current fluctuations in a quantum-dot chain reveal critical behavior during a non-equilibrium phase transition, showing non-Gaussian features at criticality.

Contribution

It demonstrates that the full counting statistics becomes non-Gaussian at the critical point, highlighting the role of dynamic critical exponents in quantum transport.

Findings

Full counting statistics is Gaussian away from the transition.

At the critical line, statistics become non-Gaussian.

Signatures of critical behavior persist in finite quantum-dot chains.

Abstract

We consider current shot noise and the full counting statistics in a chain of quantum dots which exhibits a continuous non-equilibrium phase transition as a function of the tunnel couplings of the chain with the electrodes. Using a combination of analytical and numerical methods, we establish that the full counting statistics is conventional away from the phase transition, but becomes, in a well-defined sense, essentially non-Gaussian on the critical line, where the current fluctuations are controlled by the dynamic critical exponent $z$. We find that signatures of the critical full counting statistics persist in quantum-dot chains of finite length.