Superfluidity of a perfect quantum crystal

TL;DR

This paper theoretically investigates the possibility of superfluidity in perfect quantum crystals, specifically solid helium, using a hierarchy of equations for density matrices, revealing solutions that suggest frictionless atomic flow.

Contribution

It introduces a new theoretical framework showing that perfect crystals can exhibit superfluidity, expanding understanding of quantum phases in solids.

Findings

Solutions indicate frictionless atomic flow in perfect crystals.

Superfluidity may occur in ideal solid helium.

Bifurcation analysis reveals unique solution properties.

Abstract

In recent years, experimental data were published which point to the possibility of the existence of superfluidity in solid helium. To investigate this phenomenon theoretically we employ a hierarchy of equations for reduced density matrices which describes a quantum system that is in thermodynamic equilibrium below the Bose-Einstein condensation point, the hierarchy being obtained earlier by the author. It is shown that the hierarchy admits solutions relevant to a perfect crystal (immobile) in which there is a frictionless flow of atoms, which testifies to the possibility of superfluidity in ideal solids. The solutions are studied with the help of the bifurcation method and some their peculiarities are found out. Various physical aspects of the problem, among them experimental ones, are discussed as well.