Quantum Hamilton-Jacobi Equation and Broken Symmetry in Hydrodynamics of Liquid Helium II

TL;DR

This paper explores how quantum effects and broken symmetry influence the hydrodynamics of liquid helium II, explaining phenomena like superfluidity breakdown and resolving issues in the two-fluid model at free surfaces.

Contribution

It introduces a quantum Hamilton-Jacobi framework to analyze broken symmetry and quantum fluctuations in liquid helium II's surface behavior.

Findings

Surface of He II behaves like a classical fluid due to quantum effects.

Broken symmetry at the free surface explains superfluidity breakdown at vortices.

Resolves longstanding issues in Landau's two-fluid model for rotating He II.

Abstract

Based on the quantum theory of Bohm and the phase coherence along with the mean field of Penrose and Onsager, it is shown that a free surface of He II behaves like a classical fluid. The broken symmetry of a macroscopic Bose system at the free surface in an external field is discussed in terms of the quantum fluctuations-dissipation. First, we apply this peculiarly universal behavior to explain a breakdown of superfluidity at a vortex core. Secondly, we resolve a long standing puzzle with Landau's two-fluid model on a free surface of a rotating He II in a gravitational field.