Emergent quantum Euler equation and Bose-Einstein condensates

TL;DR

This paper derives a quantum hydrodynamical framework, including the quantum Euler equation, for fluids and Bose-Einstein condensates, reproducing the Bogolyubov spectrum in the acoustic approximation.

Contribution

It introduces a new derivation method for quantum hydrodynamical equations from classical ones, applicable to both perfect and interacting fluids.

Findings

Derived quantum Euler equation for fluids.

Reproduced Bogolyubov spectrum in Bose-Einstein condensates.

Unified classical-to-quantum hydrodynamical approach.

Abstract

In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose-Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.