PhD defense by Alexandru Nicolin – Niels Bohr Institute - University of Copenhagen

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PhD defense by Alexandru Nicolin

Ever since the experimental realization of
Bose-Einstein-condensed (BEC) gases in 1995, these gases have become the
ideal playground of nonlinear scientists due to their almost unprecedented
experimental flexibility and the presence of an excellent mean-field
model, the so-called Gross-Pitaevskii (GP) equation. This equation
describes the T=0 dynamics of BEC gases and was shown to deliver very good
agreement between numerical computations and experimental results.

In my work I have investigated theoretically the dynamics of these gases
subjected to a time-dependent scattering length, focusing on mode-locking
phenomena and the emergence of Faraday waves. Mode-locking phenomena occur
due to the interplay between an external driving frequency and the
breathing mode of the condensate, while Faraday waves can be understood as
parametric instabilities triggered by an external driving field. In my
talk I will focus on simple analytical results obtained through the method
of auto-parametric resonances for the former topic and through some
peculiar properties of the Mathieu equation for the latter one.

I will end my talk with a variational model that is able to describe both
the high- and the low-density regimeS of a one-dimensional BEC gas,
reducing the partial-differential, and therefore infinitely-dimensional,
GP equation to only two ordinary differential equations.

Supervisors: Henrik Smith, Niels Bohr Institute, Mogens H. Jensen, Niels
Bohr Institute, Christopher J. Pethick, NORDITA