Bose-Einstein condensation and the glassy state
The distinction between a classical liquid and a classical ordered solid is easy and depends on their different symmetries. The distinction between a classical glass and a classical liquid is more difficult, since the glass is also disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this article an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In quantum Bose systems there is a natural parameter that can distinguish between a frozen and a non-frozen state. This is the Bose condensed fraction. In this article it is shown how to generalize this concept, in a natural way, to classical systems in order to distinguish between the glass and the liquid. A formal similarity between the ground state wave function of a Bose system and the statistical weight function enables a definition of a Bose Einstein condensed fraction in classical systems. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid. The smaller it is the larger the glassiness of the liquid.