Effective self-similar expansion for the Gross-Pitaevskii equation
Quantum Gases
2018-04-11 v2
Abstract
We consider an effective scaling approach for the free expansion of a one-dimensional quantum wave packet, consisting in a self-similar evolution to be satisfied on average, i.e. by integrating over the coordinates. A direct comparison with the solution of the Gross-Pitaevskii equation shows that the effective scaling reproduces with great accuracy the exact evolution - the actual wave function is reproduced with a fidelity close to unity - for arbitrary values of the interactions. This result represents a proof-of-concept of the effectiveness of the scaling ansatz, which has been used in different forms in the literature but never compared with the exact evolution.
Keywords
Cite
@article{arxiv.1712.00365,
title = {Effective self-similar expansion for the Gross-Pitaevskii equation},
author = {Michele Modugno and Gianni Pagnini and Manuel Angel Valle Basagoiti},
journal= {arXiv preprint arXiv:1712.00365},
year = {2018}
}
Comments
4 pages, 4 figures - revised version, accepted on PRA