Noisy quantum phase transitions: an intuitive approach

TL;DR

This paper explores how non-equilibrium 1/f charge noise affects quantum phase transitions in a resistively-shunted Josephson junction, revealing shifts, renormalizations, and effective temperature generation through intuitive methods.

Contribution

It provides a simplified, physically intuitive explanation for noise effects on quantum phase transitions, complementing previous RG-based analyses.

Findings

Noise shifts the phase transition point

Renormalizes the resistance of the system

Generates an effective temperature affecting observables

Abstract

Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers we have considered the specific case of a resistively-shunted Josephson junction driven by $1/f$ charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group (RG) approach, we found that the noise has three main effects: It shifts the phase transition, renormalizes the resistance, and generates an effective temperature. In this paper we explain how to understand these effects using simpler arguments, based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current-voltage characteristic of the junction. In the appendix we describe two possible realizations of the model with ultracold atoms confined to one dimension.