---

In this presentation, the emergence of localised, stable wave packets (solitons) is investigated in the context of the repulsive one-dimensional Bose gas. In the weakly interacting limit, the gas is approximated by the classical non-linear Schrödinger equation, of which it is known that such classical localisation occurs. A natural question to ask would be whether these classical wave packets could be reproduced starting from the quantum non-linear Schrödinger equation, and if so, which quantum mechanical wave function would produce such density profiles. Previous research has indeed attempted to do so, however, these studies had two main limitations: 1) only the attractive regime was investigated, which has limited physical significance because there is no saturation, and 2) localisation was shown only in limiting cases. In the talk, some of the mathematical steps are outlined in an attempt to overcome these two shortcomings. Besides introductory material, the talk is split into three parts according to the results obtained: 1) numerical results are discussed that show whether the desired localisation even exists outside the weakly interacting regime, 2) analytical efforts are discussed that show that Dirichlet kernels arise from the density form factor and finally 3) I will share some of the analytical efforts on simplifying general density form factors, which are of relevance when comparing magnitudes between form factor terms. It is found that mutually repulsive particles experience attraction at the macroscopic level, outside of the weakly and maximally interacting limits.

---

Tobias Bouma, University of Amsterdam
Zoom ( URL https://uni-koeln.zoom.us/j/92374710227 )
Contact: Matteo Rizzi