Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page

Non-equilibrium Lorentz gas on a curved space

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries

Techniques for the Collection and Assay of Sleep Promotion Factor in Exercised and Sleep Deprived Dogs

v, 45 leaves. Advisor: Donald B. StrattonThe problem. The Pieron Phenomenon is the production of sleep in fully rested animals after a ventricular infusion of cerebrospinal fluid (CSF) from sleep deprived animals. According to the humoral theory of sleep, this is caused by the presentation of some sleep promoting substance (factor S) which depresses the brain. The somnolence produced is accompanied by an increase in slow wave sleep (SWS). Other factors which also increase SWS, such as exercise, may also do so through some mechanism involving the accumulation of factor S. Although this molecule is known to be a polypeptide with a molecular weight under 500, the structure remains unknown, greatly complicating the exploration of these relationships. Procedure. Schedules and equipment which permit controlled administration of exercise and sleep deprivation in dogs, and techniques for the removal and storage of CSF were developed and described. An assay procedure was described which makes use of the Pieron Phenomenon and the diurnal cycle of locomotor activity in rats. Summary. This paper describes several techniques which, when appropriately combined, can be incorporated into subsequent experiments measuring the effects of a variety of parameters on the productlon of sleep promotlng substance in the CSF

Relations Among Correlation Functions in the High Temperature Phase of QCD with Broken SU(3)

Group-theoretic arguments are used to determine the dependence of two-point correlators of quark bilinears on the current quark masses. The leading difference between $\pi$ and $\delta$ correlators is found to be of order $m_s$ times a U(1)$_{\scriptscriptstyle A}$-violating correlator. These general arguments are consistent with Schaefer's observation that if U(1)$_{\scriptscriptstyle A}$ violation persists to high enough temperatures then the strange $\eta$ can be lighter than the non-strange one.Comment: 8 page

Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem

The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and obtain recurrence relations for the traces. This is possible only if the rates satisfy certain compatibility conditions. These conditions are derived and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.