# On the Lieb-Liniger model in the infinite coupling constant limit

Stephane Ouvry, Alexios P. Polychronakos

Arxiv ID: 0812.0741•Last updated: 3/6/2020

We consider the one-dimensional Lieb-Liniger model (bosons interacting via
2-body delta potentials) in the infinite coupling constant limit (the so-called
Tonks-Girardeau model). This model might be relevant as a description of atomic
Bose gases confined in a one-dimensional geometry. It is known to have a
fermionic spectrum since the N-body wavefunctions have to vanish at coinciding
points, and therefore be symmetrizations of fermionic Slater wavefunctions. We
argue that in the infinite coupling constant limit the model is
indistinguishable from free fermions, i.e., all physically accessible
observables are the same as those of free fermions. Therefore, Bose-Einstein
condensate experiments at finite energy that preserve the one-dimensional
geometry cannot test any bosonic characteristic of such a model.

#### PaperStudio AI Chat

I'm your research assistant! Ask me anything about this paper.