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A linearized version of the Hartree-Fock method is used as a probe to investigate phase transitions in fermionic systems with many-body interactions. An application to a new exactly solvable model which includes two- and three-body forces is shown.
Published experimental data on the atomic roughness of solid-vapor interfaces (SVIs) are compiled in a table and compared with the predictions of theoretical models based on the Bragg-Williams approximation (e.g., Jackson, 1958). Significant discrepancies are observed, and a new model employing site-dependent bond strengths based on many-body-interaction effects is developed and demonstrated. Predictions for Cu, Pb, and Zn are presented in extensive tables and graphs and characterized in detail: good agreement with experimental observations of anisotropic melting is obtained.
The two Griffiths' (1967) inequalities for the correlation functions of Ising ferromagnets with two-body interactions, and two other inequalities obtained by Kelly and Sherman (1968) and by Sherman (1969) are shown to hold not only for the Ashkin-Teller (1943) model but also for a generalized Ashkin-Teller model (Kihara et al., 1954) with many-body interactions involving arbitrary clusters of particles. A cluster of particles is understood to mean a collection of pairs of particles rather than a group of particles. The four generalized inequalities under consideration are presented in the form of theorems, and a new inequality is obtained.
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A cusp theorem is proved that relates the zero-separation value and slope of two-particle position correlation functions in quantum many-body systems with Coulombic interactions. The theorem is independent of the particle type and symmetry of the wave function. Its proof uses only the integral form of the Schroedinger equation and the continuity and exponential decay of the wave function. It is used to derive a sum rule for the electron-gas structure factor and an exact statement about the screening of point charges. Applications to atomic-orbital-based calculations for H2 and metallic H are described.
A review of the program in space radiation protection at the Langley Research Center is given. The relevant Boltzmann equations are given with a discussion of approximation procedures for space applications. The interaction coefficients are related to solution of the many-body Schroedinger equation with nuclear and electromagnetic forces. Various solution techniques are discussed to obtain relevant interaction cross sections with extensive comparison with experiments. Solution techniques for the Boltzmann equations are discussed in detail. Transport computer code validation is discussed through analytical benchmarking, comparison with other codes, comparison with laboratory experiments and measurements in space. Applications to lunar and Mars missions are discussed.
It is known that the infrared absorption coefficient of CO2 in the far wings is far less than what is derived from the assumption of a Lorentzian absorption profile. Sorgen and Ben-Aryeh (1972) tried to show that by incorporating the statistical many-body model into impact theory, the discrepancy between the Lorentzian absorption profile and the experimental infrared absorption coefficient can be removed. This paper attempts to show that the high frequency or short-time property of the dipole-dipole interaction cannot be adequately explained by the many-body model; in other words, the statistical model as conventionally understood is not applicable to infrared spectral lines in the far wings.
An algorithm has been developed that solves the semiconductor Maxwell-Bloch equations, without making the standard slowly-varying envelope (SVEA) and rotating-wave (RWA) approximations. It is applied to study the propagation of ultrashort pulses in semiconductor materials. The results include many-body effects due to the Coulomb interaction among the charge carriers as well as the nonlinear effects resulting from spectral hole-burning.
The rotational spectrum of v = 0 and v = 1X3Sigma(-)SH(+) was measured by laser magnetic resonance. Rotationally cold (Tr = 30 K), vibrationally excited (Tv = 3000 K) ions were generated in a corona excited supersonic expansion. The use of this source to identify ion signals is described. Improved molecular parameters were obtained; term values are presented from which astrophysically important transitions may be calculated. Accurate hyperfine parameters for both vibrational levels were determined and the vibrational dependence of the Fermi contact interaction was resolved. The hyperfine parameters agree well with recent many-body perturbation theory calculations.
A general navigation strategy for multiple autonomous robots in a bounded domain is developed analytically. Each robot is modeled as a spherical particle (i.e., an effective spatial domain about the center of mass); its interactions with other robots or with obstacles and domain boundaries are described in terms of the classical many-body problem; and a collision-avoidance strategy is derived and combined with homing, robot-robot, and robot-obstacle collision-avoidance strategies. Results from homing simulations involving (1) a single robot in a circular domain, (2) two robots in a circular domain, and (3) one robot in a domain with an obstacle are presented in graphs and briefly characterized.
Time dependent behavior of isolated system consisting of many spins in solid lattice, assuming spin-spin interactions
A comprehensive summary of a many-body, microscopic, particle-hole formalism is presented that describes coherent, subthreshold, pion production in peripheral, heavy-ion collisions. The formalism uses a new separable model transition interaction that produces Delta-hole states in either the projectile or target nucleus. Shell-model states described by harmonic oscillator functions are used in the calculation of Delta formation and decay and Lorentz-contraction effects of the nucleus not at rest are included. An analytical expression to lowest multipole order for the differential cross section is examined. The sensitivity of the theoretical results to the shell-model states is determined with preliminary shape results compared with data. The effects of higher multipoles are examined with attention paid to the second-order multipole value.
The renormalized Brueckner-Hartree-Fock (RBHF) theory for many-body nuclear systems is generalized to permit calculations for intrinsic states having permanent deformation. Both Hartree-Fock and Brueckner self-consistencies are satisfied, and details of the numerical techniques are discussed. The Hamada-Johnston interaction is used in a study of deformations, binding, size, and separation energies for several nuclei. Electromagnetic transition rates, moments, and electron scattering form factors are calculated using nuclear wave functions obtained by angular momentum projection. Comparison is made to experiment as well as to predictions of ordinary and density-dependent Hartree-Fock Theory.
The renormalized Brueckner-Hartree-Fock (RBHF) theory for many-body nuclear systems has been generalized to permit calculations for intrinsic states having permanent deformation. Both Hartree-Fock and Brueckner self-consistencies are satisfied, and details of the numerical techniques are discussed. The Hamada-Johnston interaction is used in a study of deformations, binding, size, and separation energies for several nuclei. Electromagnetic transition rates, moments, and electron scattering form factors are calculated using nuclear wave functions obtained by angular momentum projection. Comparison is made to experiment as well as to predictions of ordinary and density-dependent Hartree-Fock theory.
Analyses and interpretations of experiments which test post-Newtonian gravity are usually done under the assumption that gravity is a metric field phenomenon - a manifestation of space-time geometry. This, however, is unnecessary and one can start at a more primitive level - that there simply exists a phenomenological, gravitational, many-body equation of motion which must be determined by a package of observations. In fact, over the last couple decades, a diverse collection of solar system interbody tracking observations, supplemented by data from the binary pulsar system PSR 1913 + 16, has completely mapped out the first post-Newtonian order. After the fact, using empirically determined equations of motion, along with some observed properties of nongravitational clocks and rulers and conservation laws for energy, momentum and angular momentum, a post-Newtonian Lagrangian can be constructed, a geometrical space-time metric field conceptual interpretation can be developed, Lorentz invariance of the equations of motion can be shown, and the equations of motion are found to agree with the predictions of Einstein's gravitational theory, General Relativity, within experimental accuracy.
Many-body formulations of the equations of state are restated as a set of Saha-like equations. It is shown that the resulting equations are unique and convergent. These equations are similar to the usual Saha equations to the order of the Debye-Huckel theory. Higher order corrections, however, require a more general formulation. It is demonstrated that the positive free energy resulting from the interaction of unscreened particles in high orbits depletes the occupation of these states, without the introduction of shifted energy levels.
The possibility of nanolithography of silicon and germanium surfaces with bare carbon nanotube tips of scanning probe microscopy devices is considered with large scale classical molecular dynamics (MD) simulations employing Tersoff's reactive many-body potential for heteroatomic C/Si/Ge system. Lithography plays a key role in semiconductor manufacturing, and it is expected that future molecular and quantum electronic devices will be fabricated with nanolithographic and nanodeposition techniques. Carbon nanotubes, rolled up sheets of graphene made of carbon, are excellent candidates for use in nanolithography because they are extremely strong along axial direction and yet extremely elastic along radial direction. In the simulations, the interaction of a carbon nanotube tip with silicon surfaces is explored in two regimes. In the first scenario, the nanotubes barely touch the surface, while in the second they are pushed into the surface to make "nano holes". The first - gentle scenario mimics the nanotube-surface chemical reaction induced by the vertical mechanical manipulation of the nanotube. The second -digging - scenario intends to study the indentation profiles. The following results are reported in the two cases. In the first regime, depending on the surface impact site, two major outcomes outcomes are the selective removal of either a single surface atom or a surface dimer off the silicon surface. In the second regime, the indentation of a silicon substrate by the nanotube is observed. Upon the nanotube withdrawal, several surface silicon atoms are adsorbed at the tip of the nanotube causing significant rearrangements of atoms comprising the surface layer of the silicon substrate. The results are explained in terms of relative strength of C-C, C-Si, and Si-Si bonds. The proposed method is very robust and does not require applied voltage between the nanotube tips and the surface. The implications of the reported controllable etching and hole-creating for nanolithography on silicon are discussed in detail.
The geometrical structures of M(+) (Ar)n ions, with n = 1-14, have been studied by the minimization of a many-body potential surface with a simulated annealing procedure. The minimization method is justified for finite systems through the use of an information theory approach. It is carried out for eight potential-energy surfaces constructed with two- and three-body terms parametrized from experimental data and ab initio results. The potentials should be representative of clusters of argon atoms with first-row transition-metal monocations of varying size. The calculated geometries for M(+) = Co(+) and V(+) possess radial shells with small (ca. 4-8) first-shell coordination number. The inclusion of an ion-induced-dipole-ion-induced-dipole interaction between argon atoms raises the energy and generally lowers the symmetry of the cluster by promoting incomplete shell closure. Rotational constants as well as electric dipole and quadrupole moments are quoted for the Co(+) (Ar)n and V(+) (Ar)n predicted structures.