# Bose-Einstein condensation temperature of weakly interacting atoms

## TL;DR

This paper reviews how the critical temperature for Bose-Einstein condensation varies with system properties and trapping geometries, highlighting the use of self-similar approximants for calculations.

## Contribution

It provides a comprehensive review of defining and calculating the Bose-Einstein condensation temperature across various systems using self-similar approximants.

## Key findings

- Critical temperature depends on system properties and geometry.
- Self-similar approximants are effective for calculating critical temperature.
- Different systems require tailored definitions of phase transition temperature.

## Abstract

The critical temperature of Bose-Einstein condensation essentially depends on internal properties of the system as well as on the geometry of a trapping potential. The peculiarities of defining the phase transition temperature of Bose-Einstein condensation for different systems are reviewed, including homogenous Bose gas, trapped Bose atoms, and bosons in optical lattices. The method of self-similar approximants, convenient for calculating critical temperature, is briefly delineated.