Basic ideas of microscopic physics of liquid helium-4 and $\lambda$-transition to a coherent state

TL;DR

This paper develops a microscopic model of liquid helium-4 involving vortex fields and quasiparticles, explaining the $ ext{lambda}$-transition and accurately predicting the heat capacity near the transition point.

Contribution

It introduces a novel vortex-based microscopic framework and a quasiparticle pairing mechanism to describe helium-4's phase transitions and heat capacity behavior.

Findings

Identifies phase transition temperatures: $T_{cr}$, $T_0$, $T_ ext{lambda}$.

Derives a logarithmic temperature dependence of heat capacity near $T_ ext{lambda}$.

Numerical results align closely with experimental data.

Abstract

The article formulates the basic principles of microscopic physics of a macroscopic ensemble of interacting helium-4 atoms. The concept of a vortex field is introduced, which is caused by the motion of the particles of the electron and nuclear subsystems of atoms of the macrosystem relative to each other. It is assumed that helium-4 atoms "immersed" in the internal vortex field acquire the properties of fermionic particles due to the atomic pseudospins s=1/2 generated by the vortex. On this basis, a heuristic evolutionary model of helium-4 as an ensemble of atom-like quasiparticles with fermionic properties is constructed. As the temperature decreases, bonds are formed between pseudofermionic quasiparticles by pairing their pseudospins. The formation of a hierarchy of composite quasiparticles on this basis leads to the transition of helium-4 atoms from the gas phase to the liquid state, then to the state of incoherent Bose condensate, and finally to the state with a long-range order of atom-like quasiparticles. The structural forms of composite quasiparticles in different phases, the mechanisms of their formation, and the temperatures of these phase transitions ($T_{cr}=5.22K$, $T_0=4.14K$ and $T_\lambda=2.175K$, respectively) are determined. The ideas and calculations presented in this paper form the basis for solving the problem of the temperature dependence of the heat capacity of liquid helium-4 in both the helium-I and helium-II phases. The obtained solution has a logarithmic dependence of the heat capacity on the reduced temperature (${|1-{T/T_\lambda}|}$) in the region of the $\lambda$-point of the phase transition of helium-4 from a disordered to an ordered state. The numerical calculations of the heat capacity in the vicinity of the temperature $T_\lambda$ are in very good agreement with the experimental data.