Quantum correlation function for the noninteracting particle system.
Quantum correlation function for noninteracting n particle system in thermal equilibrium, noting Kirkwood superposition approximation and Hartree-Fock approximation
Jaen, J. K.↗
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Correlated wave functions for three-particle systems with Coulomb interaction - The muonic helium atom
A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.
Huang, K.-N.↗
Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions
The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.
Iwamoto, N.↗
Two-body problem in a many-particle system
The energy and wave functions of two-particle states in a dense plasma are essentially influenced by the surrounding medium. However, the two-particle bound-state energies may remain unshifted over a large density interval. Two simple examples are given to demonstrate the compensation of many-particle effects such as the self-energy and effective two-particle potentials in hydrogen plasmas. Neglecting self-energy and Pauli blocking, energy values that follow from numerical solutions of the Schroedinger equation with a Debye potential are obtained.
Kraeft, W. D.↗
Equilibrium Statistical Thermodynamics of a Many-Particle System Coupled to an External Scalar Field
The equilibrium thermodynamics of a many-particle assembly in the presence of an external scalar field is examined. Two types of scalar coupling are considered: an external field coupled to the particle density and an external scalar field coupled to the energy density. It is shown that the broken translational and rotational invariance of the system due to the external field is reflected in the macroscopic physics by loss of the usual extensivity property of the system and by means of anisotropy in the response of the system to changes in the system lengths or to the system shape. In addition, the assumptions used in local equilibrium analyses are shown to be incorrect in principle. Nonlocal effects due to the external field must be included in the determination of the equation of state. Simple model calculations for a system in an external gravitational field and an externally imposed temperature field are presented as illustrations.
Salvino, R. E.↗
Chemical compositions of primitive solar system particles
Chemical studies of micrometeorites are of fundamental importance primarily because atmospheric entry selection effects (such as destruction of friable objects) are less significant than those for conventional meteorites. As a result, particles that have experienced very little postaccretional processing have a significant chance of surviving the Earth encounter and subsequent collection. Thus, chemical analyses of these relatively unaltered micrometeorites may lead to a better understanding of the compositions of the most primitive materials in the solar system and thereby constrain the conditions (physical and chemical) that existed in the early solar nebula. Micrometeorites have been collected from the stratosphere, polar ices, and ocean sediments, but the stratospheric collection is the best source for the most unaltered material because they are small and are not heated to their melting points. Despite the fact that the stratospheric micrometeorites have masses in the nanogram range, a variety of microanalytical techniques have been applied to bulk chemical analyses with part-per-million sensitivity. In some cases, multi-disciplinary studies (e.g., chemistry and mineralogy) have been performed on individual particles. The first-order conclusion is that the chondrite-like particles are chemically similar to carbonaceous chondrites but in detail are distinct from members of the conventional meteorite collection. The purpose of this paper is to provide an overview of the results to date and identify important areas for further study.
Sutton, Steve R.↗
A functional random-walk model of the many- particle system
Generalized random walk method presented as master equation in nonequilibrium statistical mechanics
Hosokawa, I.↗
Exact differential equation for the density and ionization energy of a many-particle system
The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.
Levy, M.↗
Multi-Tethered Space-Based Interferometers: Particle System Model
Dynamics models are presented for a class of space-based interferometers comprised of multiple component bodies, interconnected in various arrangements, by low-mass flexible tethers of variable length. The tethered constellations are to perform coordinated rotational scanning accompanied by baseline dimensional changes, as well as spin axis realignments and spin-up/spin-down maneuvers. The mechanical idealization is a system of N point masses interconnected by massless tethers of variable length. Both extensible and inextensible tethers are considered. Expressions for system angular and linear momenta are developed. The unrestricted nonlinear motion equations are derived via Lagranges equations. Rheonomic constraints are introduced to allow prescribed motion of any degrees of freedom, and the associated physical forces are determined. The linearized equations of motion are obtained for the steady rotation of a system with extensible tethers of constant unstrained length.
Gates, Stephen S.↗
Motion of a particle in the vicinity of a triangular libration point in the Earth-Moon system
Particle motion near triangular libration point in Earth-Moon system
CELESTIAL MECHANICS↗
Mass spectra of the particle-antiparticle system with a Dirac oscillator interaction
The present view about the structure of mesons is that they are a quark-antiquark system. The mass spectrum corresponding to this system should, in principle, be given by chromodynamics, but this turns out to be a complex affair. Thus it is of some interest to consider relativistic systems of particle-antiparticle, with a simple type of interaction, which could give some insight on the spectra we can expect for mesons. This analysis is carried out when the interaction is of the Dirac oscillator type. It is shown that the Dirac equation of the antiparticle can be obtained from that of the particle by just changing the frequency omega into -omega. Following a procedure suggested by Barut, the equation for the particle-antiparticle system is derived and it is solved by a perturbation procedure. Thus, explicit expressions for the square of the mass spectra are obtained and its implications in the meson case is discussed.
Moshinsky, M.↗
Particle parameter selection system for an electrostatic particle accelerator
Particle selection system for electrostatic accelerator for hypervelocity impact testing
HYPERVELOCITY IMPACT↗
Pressure wave generation in particle-fueled combustion systems. II.
Particle motion effect in combustion produced compression wave
Busch, C. W.↗
Launch Vehicle Performance with Solid Particle Feed Systems for Atomic Propellants
An analysis of launch vehicle Gross Liftoff Weight (GLOW) using high energy density atomic propellants with solid particle feed systems was conducted. The analyses covered several propellant combinations, including atoms of aluminum (Al), boron (B). carbon (C), and hydrogen (H) stored in a solid cryogenic particle, with a cryogenic liquid as the carrier fluid. Several different weight percents (wt%) for the liquid carrier were investigated and the gross lift off weight (GLOW) of the vehicles using the solid particle feed systems were compared with a conventional 02/H2 propellant vehicle. The potential benefits and effects of feed systems using solid particles in a liquid cryogenic fluid are discussed.
Palaszewski, Bryan↗
Laser beam manifold and particle photography system for use in fluid velocity measurements
A laser beam manifold and particle photography system has been developed for use in fluid velocity measurements. The laser manifold is a device which transforms a single laser beam into several uniform parallel beams. By orienting two manifolds mutually perpendicular, an optical grid can be formed which acts as a reference for fluid velocity measurements. This optical grid is for all practical purposes totally nonperturbing to the flow. Tracer particles moving in the plane of the grid are then photographed to yield fluid velocities that can be measured relative to the optical grid. System construction and theory are presented.
Owen, R. B.↗
A high resolution holographic particle sizing system
This paper will review briefly the requirements of holography with respect to particle sizing techniques. A holographic construction system and the appropriate reconstruction system will be discussed regarding their characteristics and performance (i.e. system resolution, magnification, system aberration and correction of aberrations, and maximum total test volume). The capabilities of a commercial particle sizing system used to obtain particle sizes and distribution information from reconstructed holograms will be described and characterized. It will be shown that by using the methods described, high resolution throughout large test volumes can be achieved.
Witherow, W. K.↗
Systems of self-gravitating particles in general relativity and the concept of an equation of state
Equilibrium configurations of self-gravitating particles systems by self consistent fields method
Bonazzola, S.↗
Further evidence for the EPNT assumption
We recently proved a theorem extending the Greenberger-Horne-Zeilinger (GHZ) Theorem from multi-particle systems to two-particle systems. This proof depended upon an auxiliary assumption, the EPNT assumption (Emptiness of Paths Not Taken). According to this assumption, if there exists an Einstein-Rosen-Podolsky (EPR) element of reality that determines that a path is empty, then there can be no entity associated with the wave that travels this path (pilot-waves, empty waves, etc.) and reports information to the amplitude, when the paths recombine. We produce some further evidence in support of this assumption, which is certainly true in quantum theory. The alternative is that such a pilot-wave theory would have to violate EPR locality.
Greenberger, Daniel M.↗