Dimensional Effects on the Momentum distribution of Bosonic Trimer States

TL;DR

This paper investigates how the dimensionality of a bosonic system affects its momentum distribution, revealing universal two-body contact behavior in 2D and a unique logarithmic dependence at next-to-leading order, enabling dimensionality measurement.

Contribution

It demonstrates the universality of the two-body contact in 2D bosonic systems and identifies a distinctive logarithmic momentum dependence at next-to-leading order, proposing a new measurement scheme.

Findings

Two-body contact parameter is universal in 2D bosonic gases.

Momentum distribution exhibits a logarithmic dependence at next-to-leading order.

A scheme is proposed to measure the system's effective dimensionality.

Abstract

The momentum distribution is a powerful probe of strongly-interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few- and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution.