Dimensional crossover of nonrelativistic bosons

TL;DR

This paper explores how confining a transverse dimension affects the properties of non-relativistic bosons, focusing on the transition from three to two dimensions relevant for ultracold atom experiments, using advanced theoretical methods.

Contribution

It provides a detailed analysis of the dimensional crossover from 3D to 2D for bosons, linking scattering lengths and phase transition temperatures through Functional Renormalization Group and T-matrix calculations.

Findings

Phase transition temperature varies with transverse confinement.

Properties of lower-dimensional systems are inherited from higher dimensions.

Qualitative insights apply to various confinement geometries.

Abstract

We investigate how confining a transverse spatial dimension influences the few- and many-body properties of non-relativistic bosons with pointlike interactions. Our main focus is on the dimensional crossover from three to two dimensions, which is of relevance for ultracold atom experiments. Using Functional Renormalization Group equations and T-matrix calculations we study how the phase transition temperature changes as a function of the spatial extent of the transverse dimension and relate the 3D and 2D s-wave scattering lengths. The analysis reveals how the properties of the lower-dimensional system are inherited from the higher-dimensional one during the renormalization group evolution. We limit the discussion to confinements in a potential well with periodic boundary conditions and argue why this qualitatively captures the physics of other compactifications such as transverse harmonic confinement as in cold atom experiments.