One-dimensional Bosons in Three-dimensional Traps

TL;DR

This paper rigorously analyzes the conditions under which a low-density Bose gas in a trap behaves like a one-dimensional delta-function Bose gas, identifying five parameter regions for different behaviors based on a detailed many-body Schrödinger equation analysis.

Contribution

It provides a rigorous, parameter-based classification of 1D and 3D behaviors in trapped Bose gases, extending beyond previous variational and numerical methods.

Findings

Identification of five parameter regions for different behaviors

Rigorous analysis of the many-body Schrödinger equation

Clarification of conditions for 1D Bose gas behavior

Abstract

Recent experimental and theoretical work has indicated conditions in which a trapped, low-density Bose gas ought to behave like the 1D delta-function Bose gas solved by Lieb and Liniger. Up to now the theoretical arguments have been based on variational - perturbative ideas or numerical investigations. There are 4 parameters: density, transverse and longitudinal dimensions, and scattering length. In this paper we explicate 5 parameter regions in which various types of 1D or 3D behavior occur. Our discussion is based on a rigorous analysis of the many-body Schroedinger equation. This version of the article is a combination of the earlier 4-page arXiv version and the revised 4-page Physical Review Letters version.