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It has been proposed recently that the description of a many-body system with anharmonic coupling could be achieved through the use of the generalized Bose operators of Brandt and Greenberg (1969) directly in a second quantized form. The present study describes a new formulation of the generalized Bose operators which exploits the group theoretical content of these operators.
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.
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.
Computer methods for solving many-body and charged particle problems and nonlinear systems, classification and bibliography
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.
The usefulness of the Massively Parallel Processor (MPP) for investigation of electronic structures and hyperfine properties of atomic and condensed matter systems was explored. The major effort was directed towards the preparation of algorithms for parallelization of the computational procedure being used on serial computers for electronic structure calculations in condensed matter systems. Detailed descriptions of investigations and results are reported, including MPP adaptation of self-consistent charge extended Hueckel (SCCEH) procedure, MPP adaptation of the first-principles Hartree-Fock cluster procedure for electronic structures of large molecules and solid state systems, and MPP adaptation of the many-body procedure for atomic systems.
Investigations were carried out in two major areas during the last reporting period. Energy- and structure-related properties of small gold clusters deposited on the GaAs(110) surface were investigated using a molecular dynamics procedure. Additionally, a comparative study of the many-body potentials of silicon systems was performed.
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.
Colloidal suspensions have proven to be excellent model systems for the study of condensed matter and its phase behavior. Many of the properties of colloidal suspensions can be investigated with a systematic variation of the characteristics of the systems and, in addition, the energy, length and time scales associated with them allow for experimental probing of otherwise inaccessible regimes. The latter property also makes colloidal systems vulnerable to external influences such as gravity. Experiments performed in micro-ravity by Chaikin and Russell have been invaluable in extracting the true behavior of the systems without an external field. Weitz and Pusey intend to use mixtures of colloidal particles with additives such as polymers to induce aggregation and form weak, tenuous, highly disordered fractal structures that would be stable in the absence of gravitational forces. When dispersed in a polarizable medium, colloidal particles can ionize, emitting counterions into the solution. The standard interaction potential in these charged colloidal suspensions was first obtained by Derjaguin, Landau, Verwey and Overbeek. The DLVO potential is obtained in the mean-field linearized Poisson-Boltzmann approximation and thus has limited applicability. For more precise calculations, we have used ab initio density functional theory. In our model, colloidal particles are charged hard spheres, the counterions are described by a continuum density field and the solvent is treated as a homogeneous medium with a specified dielectric constant. We calculate the effective forces between charged colloidal particles by integrating over the solvent and counterion degrees of freedom, taking into account the direct interactions between the particles as well as particle-counterion, counterion-counterion Coulomb, counterion entropic and correlation contributions. We obtain the effective interaction potential between charged colloidal particles in different configurations. We evaluate two- and three-body forces in the bulk as well as study the influence of soft walls. We qualitatively explain the effects of the walls on the forces and demonstrate that many-body effects are negligible in our system. With adjustments in the parameters, the DLVO pair-potential can describe the results quantitatively. Besides electrostatic interactions, entropic depletion effects that arise from (hard-core) exclusion play an important role in determining the behavior of multi-component colloidal suspensions. A standard theory for depletion forces is due to Asakura and Oosawa and is based on the ideal gas approximation. To go beyond this approximation, we have studied entropic forces in molecular dynamics simulations of systems of hard spheres (the effects of the solvent have been ignored). The effective depletion forces for these systems can be found either from equilibrium distribution functions or from direct momentum transfer calculations. Our results obtained by either method show qualitative differences from the Asakura-Oosawa forces, indicating a longer range, higher value at contact and most importantly a more complicated structure, comprising of several maxima and minima. Our calculations include the determination of effective forces between two spheres, a hard sphere and a wall, and the behavior of a hard sphere near a step-edge and a corner. We also demonstrate that such entropic forces do not necessarily satisfy pairwise additivity.
The possibility of nanoscale etching and indentation of Si(001)(2x1) surface by (8,0) and (10,10) carbon nanotube tips is demonstrated, for the first time, by classical molecular dynamics simulations employing Tersoff's many-body potential for a mixed C/Si/Ge system. In the nanotube tip barely touching the surface scenario atomistic etching is observed, where as in the nanoindentation scenario nanotube tip penetrates the surface without much hindrance. The results are explained in terms of the relative strength of C-C, C-Si, and Si-Si bonds.
In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys.
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.
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.
We have studied thermal expansion of the surface layers of the hexagonally reconstructed Au (001) surface using a classical Molecular Dynamics (MD) simulation technique with an Embedded Atomic Method (EAM) type many-body potential. We find that the top-most hexagonal layer contracts as temperature increases, whereas the second layer expands or contracts depending on the system size. The magnitude of expansion coefficient of the top layer is much larger than that of the other layers. The calculated thermal expansion coefficients of the top-most layer are about -4.93 x 10(exp -5)Angstroms/Kelvin for the (262 x 227)Angstrom cluster and -3.05 x 10(exp -5)Angstroms/Kelvin for (101 x 87)Angstrom cluster. The Fast Fourier Transform (FFT) image of the atomic density shows that there exists a rotated domain of the top-most hexagonal cluster with rotation angle close to 1 degree at temperature T less than 1000Kelvin. As the temperature increases this domain undergoes a surface orientational phase transition. These predictions are in good agreement with previous phenomenological theories and experimental studies.
In order to estimate the radiation shielding effectiveness of materials it is necessary to know cosmic ray particles are broken up as they pass though these materials. The breakup of cosmic ray particles is characterized by the nuclear fragmentation cross sections, i.e. an effective geometrical cross section assigned to each target nucleus that represents its apparent size for fragmenting the incident particle. The values of these cross sections depend on the details of nuclear physics and cannot be calculated from first principles owing to the many-body nature of the interactions. The only way to determine them is to measure them. Once a sufficient number of cross sections have been measured, the systematic nature of the interactions allows other cross-sections to be estimated. The number of cross sections that contribute to the estimation of shielding effectiveness is very large 10,000. Fortunately most make minor contributions. These can be estimated from nuclear systematics. Only those who's uncertainties make significant contributions to the error in the shielding effectiveness estimations need to be measured. In the past it has proven difficult to measure light fragment production cross sections from the interactions of heavy cosmic rays owing to the size of the detectors used. We have developed a highly pixilated silicon (Si) detector system that can individually identify these light fragments while making efficient use of costly accelerator time. This system is an outgrowth of detector technology developed under a CDDF and a Code S sponsored cosmic ray experiment.
Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.
Optical interband excitonic absorption of semiconductor quantum wells (QW's) driven by a coherent pump field is investigated based on semiconductor Bloch equations. The pump field has a photon energy close to the intersubband spacing between the first two conduction subbands in the QW's. An external weak optical field probes the interband transition. The excitonic effects and pump-induced population redistribution within the conduction subbands in the QW system are included. When the density of the electron-hole pairs in the QW structure is low, the pump field induces an Autler-Townes splitting of the exciton absorption spectrum. The split size and the peak positions of the absorption doublet depend not only on the pump frequency and intensity but also on the carrier density. As the density of the electron-hole pairs is increased, the split contrast (the ratio between the maximum and minimum values) is decreased because the exciton effect is suppressed at higher densities due to the many-body screening.