# Universal Dynamics of Stochastically Driven Quantum Impurities

## TL;DR

This paper uncovers universal scaling behaviors in the dynamics of quantum impurities driven stochastically and coupled to quantum critical systems, using boundary conformal field theory and numerical validation.

## Contribution

It introduces a universal dynamical scaling form for the Loschmidt echo in stochastically driven quantum impurities, supported by analytical and numerical evidence.

## Key findings

- Universal scaling form for typical Loschmidt echo
- Rare events cause mean and typical echoes to scale differently
- Results are robust across models in the same universality class

## Abstract

We show that the dynamics of a quantum impurity subject to a stochastic drive on one side and coupled to a quantum critical system on the other display a universal behavior inherited from the quantum critical scaling. Using boundary conformal field theory, we formulate a generic ansatz for the dynamical scaling form of the typical Loschmidt echo and corroborate it with exact numerical calculations in the case of a spin impurity driven by shot noise in a quantum Ising chain. We find that due to rare events the dynamics of the mean echo can follow very different dynamical scaling than the typical echo for certain classes of drives. Our results are insensitive to irrelevant perturbations of the bulk critical model and apply to all the microscopic models in the same universality class.