Temperature dependence of the physical properties of Bose–Einstein condensed gases and liquids

Abstract

It is shown that in the presence of Bose–Einstein condensation (BEC) in any N particle system, the N particle Schrödinger wave functions of thermally occupied states are the sum of a ‘localized’ component and a ‘delocalized’ component, identical to the ground state wave function. It is shown that if N is sufficiently large, this implies that all physical properties of the system are the sum of two independent contributions from these two components. These results are used here to provide quantitative explanations of fundamental properties of BE condensed liquid 4He, unexplained even qualitatively by existing theory; why BE condensed liquid 4He is the only known physical system in which pair correlations between atomic positions reduce as it is cooled, why it is the only known liquid with sharp peaks in its dynamic structure factor, why the liquid expands with cooling and how the condensate fraction is related to the superfluid fraction. It is shown that these results also provide a relatively simple, physically transparent and quantitative explanation from first principles of macroscopic quantum effects. A new algorithm is given for the calculation of the time development of the macroscopic density of any BE condensed liquid or gas at any temperature. Unlike the Gross–Pitaevskii equation, this algorithm is valid for both strongly and weakly interacting systems. It is used here to show that macroscopic quantum interference fringes, observed between overlapping clouds of BE condensed atoms, are a necessary consequence of BEC and the N particle Schrödinger equation for the atoms in the clouds. It follows that the widely held view that these fringes are created by measurement is unnecessary. New, experimentally testable predictions are made of how the visibility of these fringes will vary with temperature.