TABLE OF CONTENTS The key to the theoretical understanding of macroscopic quantum phenomena was provided by Einstein (1924) in his prediction of the Bose Einstein condensation (BEC) of an ideal gas composed of identical bosons. Although the first experimental confirmation of the BEC of dilute gases with very weak interactions (close to an ideal gas) came much later (1995), the postulate of BEC in quantum liquids has enabled the study of superconductivity and superfluidity and has stood the test of time. [a] Here, we will give a brief account of BEC and subsequent experimental verification, before a general introduction of superfluids and superconductors.
Quantum statistical mechanics predicts that there is a phase transition in an ideal gas of identical bosons when the thermal de Broglie wavelength ? T =(2 ??/ k B T) 1/2 exceeds the mean spacing between particles. Under such conditions, bosons are stimulated by the presence of other bosons in the lowest energy state to occupy that state as well, resulting in the macroscopic occupation of a single quantum state i with energy ? i satisfying the distribution
where ? = 1/ k B T and ? is the chemical potential. The total number of particles, N, will be given by summing over the quantum states i
at any temperatures. Because the particle number is now conserved, the chemical potential is determined from (18.1.2). When T is low...
