Fluctuations and dynamics in the liquid state

We analyze two distinct features of the liquid state. While the first two moments of the density fluctuation distribution function, the mean density and the variance, are well understood this is not the case for the distribution itself. We study density fluctuations in finte observation volumes for three models of simple fluids: the hard sphere fluid, the Lennard-Jones fluid, and the lattice gas. We find that their statistics are determined by the possible presence of a nearby liquid-vapor phase transition. For fluids with such a transition the overall shape of the distribution function is analyzed within the framework of droplet theory.; The understanding of density fluctuations far away from equilibrium is particularly important to calculate the probability of observing a subvolume that does not contain any particles. The formation of such a cavity is the first step in the solvation of a solute. We study the average solvent density near hard sphere solutes and establish the existence of a transition from density enhancement for small solutes to density depletion at large solute sizes. Various solute models of increasing complexity are considered. We investigate the dependence of the solvation structure on the strength of attractive solute-solvent interactions. We find that the solvent responds linearly to such attractions, and relate this response to the density correlation function.; In a separate analysis we study the dynamics of simple liquids in the supercooled regime in order to investigate the dramatic slowing down of relaxation processes that has been observed when liquids are cooled toward their glass transition temperature. A new model system is presented that contains all the physical features of an atomistic glass former and that can be simulated on a computer up to one order of magnitude faster than existing models. This gain in simulation speed is particularly useful in the study of glasses where extremely long timescales must be considered. After analyzing familiar dynamical observables for this model we show that the relaxation times of this fluid behave differently on small and large length scales. We also study the existence of dynamical heterogeneities and their persistence in time by calculating the distribution functions of novel multi-point observables. We find that the distribution of mobility becomes significantly non-Gaussian over a wide range of timescales.