The BBGKY hierarchy in quantum statistical mechanics

It is shown that the infinite volume limit of the equilibrium reduced density matrices, shown by Ginibre to exist at low densities, satisfy the quantum time independent BBGKY hierarchy of equations. This extends analogous results for classical systems due to Gallavotti.Supported by AFOSR Contract Number F44620-71-C-0013.     

On the inverse problem in statistical mechanics

We review briefly the status of some inverse problems in classical equilibrium statistical mechanics.This paper is dedicated to Professor P. G. Bergmann on the occasion of his sixtieth birthday.Supported by NSF grant No. GP42614X.     

Coherent scattering law for dilute polymer solutions: Continued fraction formalism

The continued fraction formalism of Mori is adapted to study the coherent scattering law of dilute polymer solutions. Calculations are carried out for the Rouse chain to see the effects of the memory function. We find such effects to be significant.     

The exact velocity autocorrelation function of a model system

The velocity autocorrelation function of a particle in a model system with realistic diffusion is calculated exactly and compared with the corresponding result in the one-dimensional case. The method employed yields the result of Lebowitz and Sykes in one dimension in a very simple manner.Research Supported by NSF Grant No. R019881001.     

Effects of memory on the coherent scattering function for the rouse–zimm model of dilute polymer solutions

We study the effect of the memory function on the coherent scattering function of a dilute polymer solution, taking into account hydrodynamic interactions among the polymer segments. The line shape, given by a sum of two exponentials, is very accurate numerically for ka ? 3 (with a the length of a polymer segment) and for times such that ω₀(k)t ? 1.5 [with ω₀(k) the initial slope]. However, this approximation to the scattering function is not nearly so accurate at the smaller values of ka encountered in light scattering experiments. The amplitudes and relaxation times associated with the two exponentials are found to be markedly dependent on the strength of the hydrodynamic interactions.     

Stochastic model of a one-dimensional fluid

A one-dimensional point process with correlations constructed via a geometrical rule is shown to behave like a fluid at equilibrium. The equation of state is calculated and the “inverse problem” of finding an interaction potential underlying the system is considered. The effective potential is found to be dependent on macroscopic parameters via a dependence on the density of the system.