Derivation of the Euler Equations from Quantum Dynamics

TL;DR

This paper rigorously derives the classical Euler equations from quantum fermionic many-body dynamics, bridging quantum mechanics and fluid dynamics under specific assumptions.

Contribution

It provides a novel derivation of Euler equations from quantum fermionic systems based on physical and statistical assumptions.

Findings

Derivation of Euler equations from quantum fermionic systems

Establishment of assumptions linking quantum dynamics to classical fluid equations

Bridging quantum mechanics and classical fluid dynamics

Abstract

We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the solution of the Euler equations for the given initial data. The second type are a number of reasonable conjectures on the statistical mechanics and dynamics of the Fermion Hamiltonian.