Effective self-similar expansion for the Gross-Pitaevskii equation

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.

4 pages, 4 figures - revised version, accepted on PRA

References in corpus (1)

• Theory of ultracold Fermi gases

Cited by in corpus (7)

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• Non-linear mixing of Bogoliubov modes in a bosonic Josephson junction
• All-Optical Matter-Wave Lens using Time-Averaged Potentials
• Exactly solvable Gross-Pitaevskii type equations
• Effective self-similar expansion of a Bose-Einstein condensate: Free space vs confined geometries
• Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases
• Scaling dynamics of the ultracold Bose gas