Quasicondensation reexamined

TL;DR

This paper investigates the nature of quasicondensation across different dimensions, revealing its dependence on system geometry and size, and clarifying its behavior in ideal Bose gases below quantum degeneracy temperature.

Contribution

It provides a detailed analysis of quasicondensation's relation to dimensionality and system geometry, extending understanding beyond previous models.

Findings

Quasicondensation occurs in 1D systems regardless of interactions.

In higher dimensions, the second eigenvalue diminishes as N^(-γ), vanishing in the thermodynamic limit.

In 1D, the eigenvalue ratio decreases logarithmically with system size.

Abstract

We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions - exists in repulsive, attractive or in non-interacting Bose gas in some range of temperatures below characteristic temperature of the quantum degeneracy. Based on this observation we analyze the quasicondensation in terms of a ratio of the two largest eigenvalues of the single particle density matrix for the ideal gas. We show that in the thermodynamic limit in higher dimensions the second largest eigenvalue vanishes (as compared to the first one) with total number of particles as $\simeq N^{-\gamma}$ whereas goes to zero only logarithmically in one dimension. We also study the effect of quasicondensation for various geometries of the system: from quasi-1D elongated one, through spherically symmetric 3D case to quasi-2D pancake-like geometry.