Bose-Einstein Condensation of strongly interacting bosons: from liquid ${}^4$He to QCD monopoles

TL;DR

This paper demonstrates the robustness of Feynman's universal action concept at the BEC transition for both liquid helium and QCD monopoles, providing new insights into critical temperature dependence and phase transition mechanisms.

Contribution

It extends Feynman's BEC theory to strongly interacting systems like liquid helium and QCD monopoles, offering a unified model for critical behavior and phase transitions.

Findings

Critical action is universal for interacting and noninteracting bosons.

Accurate density dependence of critical temperature in liquid helium.

Proposed lattice tests for BEC of monopoles in QCD.

Abstract

Starting from classic work of Feynman on the $\lambda$-point of liquid Helium, we show that his idea of universal action per particle at the BEC transition point is much more robust that it was known before. Using a simple "moving string model" for supercurrent and calculating the action, both semiclassically and numerically, we show that the critical action is the same for noninteracting and strongly interacting systems such as liquid ${}^4$He. Inversely, one can obtain accurate dependence of critical temperature on density: one important consequence is that high density (solid) He cannot be a BEC state of He atoms, with upper density accurately matching the observations. We then use this model for the deconfinement phase transition of QCD-like gauge theories, treated as BEC of (color)magnetic monopoles. We start with Feynman-like approach without interaction, estimating the monopole mass at $T_c$. Then we include monopole's Coulomb repulsion, and formulate a relation between the mass, density and coupling which should be fulfilled at the deconfinement point. We end up proposing various ways to test on the lattice whether it is indeed the BEC point for monopoles.