Spontaneous Symmetry Breaking in Superfluid Helium-4

TL;DR

This paper derives an analytical expression for the critical temperature of spontaneous symmetry breaking in superfluid helium-4, showing close agreement with experimental lambda temperature.

Contribution

It provides a new formula linking critical temperature to physical parameters of a Bose system, accurately predicting superfluid helium-4's transition temperature.

Findings

Predicted Tc for helium-4 is 2.194 K, close to experimental 2.1768 K.

Deviation between predicted and experimental Tc is less than 1%.

The formula relates Tc to density, mass, and sphere diameter of bosons.

Abstract

We derive an analytical expression for a critical temperature of spontaneous symmetry breaking in a repulsive hard-core interacting Bose system. We show that the critical temperature of spontaneous symmetry breaking in a hard-core interacting Bose system is determined by the three physical parameters: the density of Bose liquid at absolute zero (rho_0), the mass (m) and the hard sphere diameter (sigma) of a boson. The formula that we have derived is Tc = rho_0 pi hbar^2 sigma / m^2 kB. We report Tc of liquid helium-4 is 2.194 K, which is significantly close to the lambda temperature of 2.1768 K. The deviation between the predicted and experimental values of the lambda temperature is less than 1%.