Emergence of fluctuating hydrodynamics in chaotic quantum systems

TL;DR

This paper demonstrates that large-scale fluctuations in chaotic quantum systems exhibit emergent hydrodynamic behavior, aligning with macroscopic fluctuation theory predictions and enabling extraction of diffusion constants from quantum simulations.

Contribution

The study extends macroscopic fluctuation theory to chaotic quantum systems, showing emergent hydrodynamics and providing a method to quantify diffusion through quantum simulations.

Findings

Quantum fluctuations match MFT predictions

Diffusion constants can be extracted from fluctuation data

Large-scale quantum fluctuations exhibit hydrodynamic behavior

Abstract

A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in hard-core boson ladders, contrasting systems with ballistic and chaotic dynamics. We find excellent agreement between our results and MFT predictions, which allows us to accurately extract diffusion constants from fluctuation growth. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior, expanding the applicability of MFT to the quantum regime.