Concepts of Intertial and Gravitational Mass

The general relativistic notion of gravitational and inertial mass is discussed from the general viewpoint of the tidal forces implicit in the curvature and the Einstein field equations within ponderable matter. A simple yet rigorously general derivation is given for the Tolman gravitational mass viewpoint wherein the computation of gravitational mass requires both a rest energy contribution (the inertial mass) and a pressure contribution. The pressure contribution is extremely small under normal conditions which implies the equality of gravitational and inertial mass to a high degree of accuracy. However, the pressure contribution is substantial for conformal symmetric systems such as Maxwell radiation, whose constituent photons are massless. Implications of the Tolman mass for standard cosmology and standard high energy particle physics models are briefly explored.Comment: LaTeX Format No Figure

Nuclear Abundances in Metallic Hydride Electrodes of Electrolytic Chemical Cells

Low energy nuclear transmutations have been reported in experimental chemical electrolytic cells employing metallic hydride electrodes. Assuming that the nuclear transmutations are induced by ultra-low momentum neutron absorption, the expected chemical cell nuclear abundances are discussed on the basis of a neutron optical potential model. The theoretical results are in satisfactory agreement with available experimental chemical cell data. Some implications of these laboratory nuclear transmutations for r- s-process models of the neutron induced solar system and galactic nuclear abundance are briefly explored.Comment: 6 pages *.TeX format, 3 figures *.eps forma

Theoretical Standard Model Rates of Proton to Neutron Conversions Near Metallic Hydride Surfaces

The process of radiation induced electron capture by protons or deuterons producing new ultra low momentum neutrons and neutrinos may be theoretically described within the standard field theoretical model of electroweak interactions. For protons or deuterons in the neighborhoods of surfaces of condensed matter metallic hydride cathodes, such conversions are determined in part by the collective plasma modes of the participating charged particles, e.g. electrons and protons. The radiation energy required for such low energy nuclear reactions may be supplied by the applied voltage required to push a strong charged current across a metallic hydride surface employed as a cathode within a chemical cell. The electroweak rates of the resulting ultra low momentum neutron production are computed from these considerations.Comment: ReVTeX format 12 pages and 4 *.eps figure

Absorption of Nuclear Gamma Radiation by Heavy Electrons on Metallic Hydride Surfaces

Low energy nuclear reactions in the neighborhood of metallic hydride surfaces may be induced by ultra-low momentum neutrons. Heavy electrons are absorbed by protons or deuterons producing ultra low momentum neutrons and neutrinos. The required electron mass renormalization is provided by the interaction between surface electron plasma oscillations and surface proton oscillations. The resulting neutron catalyzed low energy nuclear reactions emit copious prompt gamma radiation. The heavy electrons which induce the initially produced neutrons also strongly absorb the prompt nuclear gamma radiation, re-emitting soft photons. Nuclear hard photon radiation away from the metallic hydride surfaces is thereby strongly suppressed.Comment: ReVTeX format 6 pages no figure

Bose Condensates in TOP Traps Exhibit Circulating Superfluid Flows

For spin one atoms localized in a quadrapole magnetic field gradient, the atoms may be impeded from spin flipping their way out from the center of the trap by the application of a rotating uniform magnetic field. From a quantum mechanical viewpoint, such a trap for a Bose condensate is equivalent to having a superfluid in a rotating bucket. Vorticity is then expected to be induced in the condensate fluid flow without the application of any further external perturbations.Comment: 4 page

Bose Condensation and Superfluidity in Finite Rotating Bose Systems

There is a long standing problem about how close a connection exists between superfluidity and Bose condensation. Employing recent technology, for the case of confined finite Bose condensed systems in TOP traps, these questions concerning superfluidity and Bose condensation can be partially resolved if the velocity profile of the trapped atoms can be directly measured.Comment: 5 page

Physical Kinetics of Ferroelectric Hysteresis

The physical kinetics of single domain ferroelectric materials are studied using Landau-Khalatnikov equation. The hysteretic curves are obtained numerically. The effective coercive electric field theoretically varies with the driving amplitude and frequency. The effects of thermal noise are explored using the Fokker-Planck kinetic equation. The ferroelectric switching times are discussed and Quantum effects are briefly explored.Comment: ReVTeX with three *eps figures. Six page

Quantum Interference and the Trapped Bose Condensed System

In experiments involving Bose condensed atoms trapped in magnetic bottles, plugging the hole in the bottle potential with a LASER beam produces a new potential with two minima, and thus a condensate order parameter (i.e. wave function) with two maxima. When the trapping potential is removed and the condensate explodes away from the trap, the two wave function maxima act as two coherent sources which exhibit amplitude interference. A simplified theoretical treatment of this experimental effect is provided by considering momentum distributions.Comment: 4 page

Szeg\"o via Jacobi

At present there exist numerous different approaches to results on Toeplitz determinants of the type of Szeg\"o's strong limit theorem. The intention of this paper is to show that Jacobi's theorem on the minors of the inverse matrix remains one of the most comfortable tools for tackling the matter. We repeat a known proof of the Borodin-Okounkov formula and thus of the strong Szeg\"o limit theorem that is based on Jacobi's theorem. We then use Jacobi's theorem to derive exact and asymptotic formulas for Toeplitz determinants generated by functions with nonzero winding number. This derivation is new and completely elementaryComment: 15 pages, LaTe

Landau-Khalatnikov Circuit model for Ferroelectric Hysteresis

We present the circuit equivalent of the Landau-Khalatnikov dynamical ferroelectric model. The differential equation for hysteretic behavior is subject to numerical computer simulations. The size and shape of the simulated hysteretic loops depends strongly on the frequency and the amplitude of the driving electric field. This dependence makes the experimental extraction of the coercive electric field difficult. The bifurcation of the driven Landau-Khalatnikov model is explained in detail.Comment: ReVTeX4 format, 6 pages, 6 figures *.ep