Spatial bose condensation: universal features in size distribution of clusters

We present the computation of the mean cluster size distribution in quantum systems displaying spatial Bose-Einstein condensation (BEC). The key result is the sudden appearance of a bimodal cluster weight distribution precisely at the temperature at which the specific heat curve is peaked. We suggest that the bimodality in mean weight distribution of clusters can serve as a new criteria for spatial BEC in finite systems

Molecular theory for freezing transition of hard ellipsoid and hard dumbbell molecules

We present a density-functional-variational theory to investigate the nature of the freezing transition in a system consisting of hard ellipsoid and hard dumbbell molecules. We predict the isotropic-plastic and the isotropic-nematic phase coexistence for hard ellipsoid molecules. The results are in fair agreement with Monte Carlo simulations. For hard dumbbell molecules we find an orientationally disordered fcc lattice phase for bond length L/σ in the range 0<L/σ≤0.26

Bimodality of cluster-size distribution and condensation in a finite Lennard-Jones system

The complete summation of Mayer's expression for the canonical-ensemble partition function for a finite number N of particles, in terms of reducible cluster integrals bk (1≤k≤N), is performed with a recursion formula. The bk required for this are themselves obtained by use of the same technique in the summation of Mayer's expression for them, in the volume-independent case, in terms of star (i.e., irreducible cluster) integrals ßj (1≤j≤k-1). Below the critical temperature the results, obtained with use of all the star integrals that have been evaluated for the Lennard-Jones potential, display features indicative of vapor condensation at appropriate densities, i.e., bimodality in the size distribution of Mayer's mathematical clusters and remarkable constancy (for small N) in the pressure isotherms. Thus the lower-order star integrals alone suffice for the appearance of the phenomenon of vapor condensation in the theoretical results. Indeed the first star integral β1 alone (corresponding to a "tree approximation" for the cluster integrals bk) is found to suffice. This suggests that the cooperative essence of the first-order transition from vapor to liquid is to be attributed primarily to a cascade in chain branching

Bimodality and long-range order in ideal Bose systems

The cluster expansion for the classical and the quantum canonical partition function are related to the Bell polynomials. This observation is exploited in derivation of a set of recursion relations that render tractable numerical evaluation of quantities such as mean cluster size distributions and pressure isotherms. The exact volume dependences of properties of an ideal Bose gas are calculated under periodic boundary conditions. Numerical calculations with volume-independent cluster integrals show bimodal distributions in the mean cluster weight for two- and three-dimensional ideal Bose gases at sufficiently low temperature and high density. The variation of the size at which the liquid (condensate) peak appears indicates that the liquid clusters are macroscopic in macroscopic systems. The similarity between the Bose-Einstein condensation and the sol→gel transition in nonlinear chemically polymerizing systems is discussed. When the exact volume dependence of the cluster integrals is taken into account, the mean cluster weight distribution becomes "chair shaped" rather than bimodal and displays no diagonal long-range order in the canonical ensemble. The "Kac density" for an ideal Bose gas implies that in the canonical ensemble the Ursell function satisfies a cluster property in the limit in which the coordinates of the particles are widely separated