# Condensation and superfluidity of $SU(N)$ Bose gas

## TL;DR

This paper investigates the properties of condensate and superfluid densities in an $SU(N)$ Bose gas, using large-$N$ expansion and Monte Carlo simulations to analyze thermal fluctuations and compare theoretical predictions with numerical results.

## Contribution

It introduces a large-$N$ expansion approach to derive a general expression for superfluid density in multi-component Bose gases, incorporating thermal fluctuations.

## Key findings

- Superfluid density formula reproduces Landau's at low temperatures.
- Numerical results agree qualitatively with Monte Carlo simulations.
- Thermal fluctuations significantly affect superfluid properties.

## Abstract

We perform the comprehensive comparison of properties of the condensate and superfluid densities for the $N$-component three-dimensional Bose gas with the symmetric inter- and intraspecies short-range interaction between particles. In particular, based on the large-$N$ expansion approach for many-boson systems we obtain general expression for density of the superfluid component that at very low temperatures reproduce the well-know Landau's formula and non-trivially includes the thermal fluctuations in the finite-temperature region, and compare it to the condensate density calculated previously. The numerically evaluated temperature dependencies are in a qualitatively good agreement with the results of Monte Carlo simulations.