The name is absent

Chapter 1

Introduction

In the past decade, ultracold atomic physics is characterized by an impressive amount of
experimental progresses in both Bose and Fermi gases. As experiments keep probing ul-
tracold atomic gases under an increasing variety of situations, substantial theoretical ef-
forts are being spent to characterize the experiments as well as in investigating underlying
physics. Among these theoretical efforts, much is conducted by analytical means, with
the whole range of quantum statistical tools. As it always happens to the case of com-
plex physical phenomena, analytical methods face severe limitations whenever genuinely
поп-perturbative and strongly nonlinear effects need to be quantitatively addressed. Under
these circumstances numerical measures become mandatory. The aim of this thesis is to
introduce a couple of efficient numerical schemes which we use in seeking the mean-field
ground state of Bose-Einstein condensates (BECs) and ultracold Fermi gases.

The mean field theory is a powerful, yet simple tool for many-body problem. For the

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