Derivation of Euler equations from quantum and classical microscopic dynamics

TL;DR

This paper derives Euler equations from microscopic quantum and classical dynamics of a disordered harmonic chain, showing how macroscopic transport emerges from microscopic Hamiltonian systems in a hyperbolic scaling limit.

Contribution

It extends previous work by controlling fluctuations and broadening initial state classes, strengthening the derivation of Euler equations from microscopic models.

Findings

Euler equations derived from microscopic dynamics

Control of fluctuations around the mean

Broader class of initial states allowed

Abstract

We derive Euler equations from a Hamiltonian microscopic dynamics. The microscopic system is a one-dimensional disordered harmonic chain, and the dynamics is either quantum or classical. This chain is an Anderson insulator with a symmetry protected mode: Thermal fluctuations are frozen while the low modes ensure the transport of elongation, momentum and mechanical energy, that evolve according to Euler equations in an hyperbolic scaling limit. In this paper, we strengthen considerably our previous results, where we established a limit in mean starting from a local Gibbs state: We now control the second moment of the fluctuations around the average, yielding a limit in probability, and we enlarge the class of admissible initial states.