BEC to basics

Tian De Cao

The basic principle of superconductivity is suggested in this paper. There have been two vital wrong suggestions on the basic principle, one is the relation between superconductivity and the Bose-Einstein condensation (BEC), and another is the relation between superconductivity and pseudogap.

Anonymous

Vanderlei Salvador Bagnato, K. M. F. Magalhães, Jorge Amin Seman +5 more

This text corresponds to part of the course presented at the ELAF XXXVIII. It is composed of work previously done along the years. The level of this introduction follows the last year of undergraduate and first year of graduate courses. We apologize to the experts on this field, but the idea here is to provide the basic principles and tools for students just getting involved with this topic. For those interested in a deeper reading on the subject, we strongly recommend the review article published by Courteille, Bagnato and Yukalov [1] from which part of this text was extracted. The lecture is divided in three parts: an introduction, the basic concepts of Bose‐Einstein Condensation and information about making and probing BECs.

Philip F. Schewe

David Guéry-Odelin, Thierry Lahaye

This chapter introduces basic notions about Bose-Einstein condensates (BECs). One first studies ideal Bose gases, putting an emphasis on the role of the trapping geometry and of the dimensionality. One also introduces the correlation functions characterizing coherence. The second section deals with weakly-interacting BECs, which are described, in a mean-field approach, by the so-called Gross-Pitaevskii equation. This equation is derived and applied to a variety of experimentally relevant situations. The third section deals with beyond-mean-field effects that appear when the interactions are stronger, and introduces in particular the Bogolubov approximation. The last section is devoted to the study of BECs in double-well potentials, a situation inspired from condensed matter systems where beyond-mean-field effects can appear quite easily, and which remains simple enough to be studied theoretically in details.