Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.     

Determination of activity coefficients for ammonium chloride at 25°C

Precise values of the activity coefficients of aqueous ammonium chloride solutions at 25°C determined from emf measurements of cells with transference are reported for the concentration range 0 to 0.2m. The results show no anomalous behavior with respect to the Debye-Hückel limiting law. An interpretation of excess thermodynamic functions of potassium and ammonium chloride solutions is made in terms of ionic influences on solvent structure. The relative order of activity coefficients for the R ₄ NCl series up to 0.1m is shown to be (NH ₄ Cl)>(Me ₄ NCl)>(Et ₄ NCl)>(n-Bu ₄ NCl).     

Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas

In the example of a weakly imperfect Bose gas, we discuss the mechanism of establishing thermodynamic equilibrium for a chaotic set of quantum vortex filaments. We assume that the dynamics of the Bose condensate is described by the Gross–Pitaevsky equation with an additional noise satisfying the fluctuation–dissipation theorem. In considering a vortex filament as the intersection line of surfaces on which the real and imaginary parts of the order parameter (x,t) vanish, we obtain an equation of the Langevin type for elements of the vortex filament with an appropriately transformed random force. The Fokker–Planck equation for the probability density has a solution given by the Gibbs distribution at the temperature of the Bose condensate. In other words, when the Bose condensate is in thermal equilibrium and no other random actions exist, the system of vortices is also in thermal equilibrium.     

Effect of H/D-isotope substitution on the solubility and solvation thermodynamics of krypton in methanol solutions of carbamide

The solubility of gaseous krypton in CO(NH₂)₂—CH₃OH (CD₃OH) and CO(ND₂)₂—CH₃OD solutions with carbamide concentrations of up to 1.5 solvomolality units (0.026 mole fractions) was measured at 278, 288, 298, 308, and 318 K and at a partial gas pressure of 101325 Pa. The thermodynamic functions of dissolution (solvation) of krypton and the standard Setchenov coefficients were calculated. The solvation of Kr molecules increases upon deuterium substitution and with an increase in the temperature and carbamide concentration. In these solutions, specific contacts between the carbamide and methanol molecules play the predominant role.     

Determining Liquid Structure from the Tail of the Direct Correlation Function

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard-sphere fluid for all distances r by specifying only the tail of the direct correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the out projection of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein–Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard-core Yukawa fluid are discussed.     

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.     

Solid–liquid equilibria based on an equation of state for chain fluids

Solid–liquid equilibria were studied using an equation of state previously developed for fluids containing chain-like molecules. The method was used to correlate solubilities of normal alkanes and aromatic compounds with high molecular mass in hydrocarbon solvents. With one temperature independent parameter for the interaction energy, good agreement can be obtained between calculated results and experimental data for selected systems.     

Enthalpies of Formation of the Tellurites of the Rare Earths Gd, Tb, Dy, Tm and Yb

By using a DSK of the French firm Seteram, the standard enthalpies of formation of 5 tellurites and 5 tetratellurites of the rare earths Gd, Tb, Dy, Tm and Yb were determined for the first time. Three parallel determinations for each sample were compared. The results are very similar, which is an indication of the great reliability of the method used and the correctness of the data obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Symmetrization of the nonlinear system of gas dynamics equations

We describe a method for representing the nonlinear system of gas dynamics equations in quasilinear form with symmetric coefficient matrices and, moreover, with a positive definite matrix at the time derivative.