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arXiv · 1712.00365

Effective self-similar expansion for the Gross-Pitaevskii equation

Michele Modugno·Gianni Pagnini·Manuel Angel Valle Basagoiti
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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.

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Michele Modugno, Gianni Pagnini, Manuel Angel Valle Basagoiti. 2017-12-01. Effective self-similar expansion for the Gross-Pitaevskii equation. https://doi.org/10.1103/physreva.97.043604

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