A Brief History of Our Understanding of BEC: From Bose to Beliaev

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We review how our current ideas about BEC developed in the early period 1925-1965, which had the specific goal of understanding superfluid $^4$He. This history is presented by commenting on the key contributions made by Einstein, Fritz London, Tisza, Landau, Bogoliubov, Oliver Penrose and Feynman. We emphasize the emergence of the concept of a macroscopic wavefunction describing the condensate. Starting with the fundamental work of Beliaev in 1957, the period 1957-1965 was a golden era for theoretical studies of interacting Bose-condensed gases. This work provided a sound conceptual basis for understanding the properties of trapped atomic gases which were discovered thirty years later.
Lecture given at the BEC Varenna Summer School, July 7-17, 1998. To be published in "Bose-Einstein Condensation in Atomic Gases", ed. by M.Inguscio, S.Stringari and C. Wieman (Italian Physical Society, 1999)

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