# Instanton Liquid at Finite Temperature and Chemical Potential of Quarks

## TL;DR

This paper investigates how the instanton liquid's density and gluon condensate change with temperature and quark chemical potential using a variational approach and caloron ensembles.

## Contribution

It introduces a method to analyze the instanton liquid at finite temperature and chemical potential considering calorons and effective quark Lagrangian.

## Key findings

- Instanton liquid density varies with temperature and chemical potential.
- Gluon condensate dependence on thermodynamic parameters is characterized.
- Caloron ensemble dominates the finite temperature instanton contributions.

## Abstract

Instanton liquid in heated and strongly interacting matter is studied using the variational principle. The dependence of the instanton liquid density (gluon condensate) on the temperature and the quark chemical potential is determined under the assumption that, at finite temperatures, the dominant contribution is given by an ensemble of calorons. The respective one-loop effective quark Lagrangian is used.