Equation of state of the one- and three-dimensional Bose-Bose gases

TL;DR

This paper derives the equation of state for one- and three-dimensional Bose-Bose gases using quantum field theory, revealing solitonic solutions and temperature-dependent properties of quantum droplets.

Contribution

It provides a novel analytical framework for describing Bose-Bose mixtures, including solitonic solutions and finite-temperature effects, using effective quantum field theory and dimensional regularization.

Findings

Existence of self-trapped solitonic droplets in 1D.

Analytical solutions of the nonlinear Schrödinger equation for Bose-Bose mixtures.

Nontrivial dependence of pressure and particle number on chemical potential at low temperature.

Abstract

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero-temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schr\"odinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic-droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the inter-species coupling constants.