Bose-Einstein condensation in perfect crystals

TL;DR

This paper investigates Bose-Einstein condensation in perfect crystals using a hierarchy of equations for reduced density matrices, analyzing phase transitions and properties of condensate crystals at zero temperature.

Contribution

It introduces a new hierarchy of equations for equilibrium quantum systems and applies bifurcation methods to study Bose-Einstein condensation in perfect crystals.

Findings

Condensate properties at zero temperature are characterized.

Bifurcation analysis reveals phase transition scenarios.

Superfluid states may arise from one or two phase transitions.

Abstract

To investigate the phenomenon of Bose-Einstein condensation in perfect crystals a hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system is employed, the hierarchy being obtained earlier by the author. The thermodynamics of a crystal with a condensate and the one of a crystal with no condensate are constructed in parallel, which is required for studying the phase transition involving Bose-Einstein condensation. The transition is analysed also with the help of the Landau theory of phase transitions which shows that a superfluid state can result either from two consecutive phase transitions or from only one. To demonstrate how the general equations obtained can be applied for a concrete crystal the bifurcation method for solving the equations is utilized. New results concerning properties of the condensate crystals at zero temperature are obtained as well. In the concluding section, the physical concept of the condensate is discussed.