Many-body Chaos in Thermalised Fluids

Abstract

Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we prove that in thermalised flows $\lambda \propto \sqrt{T}$, in agreement with results from frustrated spin systems. This reveals an underlying universality and provides evidence for recent conjectures on the thermal scaling of $\lambda$. We also reconcile seemingly disparate effects -- equilibration on one hand and pushing systems out-of-equilibrium on the other -- of many-body chaos by relating $\lambda$ to $T$ through the dynamical structures of the flow.

Minor changes; Published in Physical Review Letters:

References in corpus (11)

• Burgers Turbulence
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Quantum chaos on a critical Fermi surface
• Thermal diffusivity and chaos in metals without quasiparticles
• Temperature dependence of butterfly effect in a classical many-body system
• Classical many-body chaos with and without quasiparticles
• Two-fluid model of the truncated Euler Equations
• Suppressing thermalization and constructing weak solutions in truncated inviscid equations of hydrodynamics: Lessons from the Burgers equation
• Constraints on hydrodynamics from many-body quantum chaos
• The Onset of Thermalisation in Finite-Dimensional Equations of Hydrodynamics: Insights from the Burgers Equation
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

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