VTechWorks Repository :: Browsing by Author "Bowen, Samuel P."

Browsing by Author "Bowen, Samuel P."

Now showing 1 - 19 of 19

Analytic approximation to the ground-state energy of the Anderson model
Mancini, Jay D.; Massano, William J.; Potter, Charles D.; Bowen, Samuel P. (American Physical Society, 1988-09)
Using the nonperturbative Lanczos recursion scheme an analytic approximation to the ground-state energy of the single-impurity Anderson model is obtained. Calculations are carried out to a 5x5 matrix truncation. Comparisons are made with the exact Bethe-ansatz result.
Application of classical non-linear Liouville dynamic approximations
Harter, Terry Lee (Virginia Polytechnic Institute and State University, 1988)
This dissertation examines the application of the Liouville operator to problems in classical mechanics. An approximation scheme or methodology is sought that would allow the calculation of the position and momentum of an object at a specified later time, given the initial values of the object's position and momentum at some specified earlier time. The approximation scheme utilizes matrix techniques to represent the Liouville operator. An approximation scheme using the Liouville operator is formulated and applied to several simple one-dimensional physical problems, whose solution is obtainable in terms of known analytic functions. The scheme is shown to be extendable relative to cross products and powers of the variables involved. The approximation scheme is applied to a more complicated one-dimensional problem, a quartic perturbed simple harmonic oscillator, whose solution is not capable of being expressed in terms of simple analytic functions. Data produced by the application of the approximation scheme to the perturbed quartic harmonic oscillator is analyzed statistically and graphically. The scheme is reapplied to the solution of the same problem with the incorporation of a drag term, and the results analyzed. The scheme is then applied to a simple physical pendulum having a functionalized potential in order to ascertain the limits of the approximation technique. The approximation scheme is next applied to a two-dimensional non-perturbed Kepler problem. The data produced is analyzed statistically and graphically. Conclusions are drawn and suggestions are made in order to continue the research in several of the areas presented.
Application of the connected-moment expansion to single-impurity Anderson Hamiltonians
Massano, William J.; Bowen, Samuel P.; Mancini, Jay D. (American Physical Society, 1989-04)
We use the connected-moment expansion, recently developed by Cioslowski [Phys. Rev. Lett. 58, 83 (1987)], to investigate the ground-state energy of the single-impurity Anderson model. It is found that the moment expansion obtained for this Hamiltonian is not a Stieltjes series and thus does not provide a useful method for estimating ground-state energies.
An application of the Liouville resolvent method to the study of fermion-boson couplings
Bressler, Barry Lee (Virginia Polytechnic Institute and State University, 1986)
The Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a Hilbert space and that represent transitions between many-particle states. These commutators produce linear combinations of stepping operators, so the results can be arrayed as matrix elements of the Liouville operator L̂ in the Hilbert space of stepping operators. The resulting L̂ matrix is usually of infinite order, and in principle its eigenvalues and eigenvectors can be used to construct the Green function from the L̂ resolvent matrix. Approximations are usually necessary, at least in the form of truncation of the L̂ matrix, and if one produces a sequence of such matrices of increasing order and calculates the eigenvalues and eigenvectors of these matrices, a sequence of approximations for the L̂ resolvent matrix can be produced. This sequence is mathematically guaranteed to converge to the exact result for the L̂ resolvent matrix (except at its singularities). The accuracy of an approximation depends on the order of the matrix at which the sequence is truncated. Application of the method to a Hamiltonian representing interactions between fermions and bosons involves complications arising from the large number of terms generated by the commutation properties of boson operators. This dissertation describes the method and its use in the study of fermion-boson couplings. Approximations to second order in stepping operators are calculated for simplified Froehlich and Lee models. Limited thermodynamic results are obtained from the Lee model. Exact energy eigenvalues are obtained by operator algebra for simplified Froehlich, Lee and Dirac models. These exact solutions comprise the main contribution of this research and will prove to be valuable starting points for further research. Suggestions are made for further research.
Configuration fluctuations and the dilute-magnetic-alloy problem
Bowen, Samuel P. (American Physical Society, 1978-10)
A new theoretical treatment of the Anderson model of transition-metal or rare-earth impurities in a simple metal is presented. This study treats the impurity Coulomb correlation exactly and the host impurity coupling to lowest order in the sense of a self-consistent degenerate perturbation theory. The central result of this work is that if an impurity interconfigurational excitation energy (ICEE) is close to the Fermi energy in the atomic limit, a temperature-dependent shift of the ICEE is found for the interacting system. This temperature-dependent shift is shown to give a good description of the experimental observations on dilute magnetic alloys.
Convergent methods for calculating thermodynamic Green functions
Bowen, Samuel P.; Williams, Clayton D.; Mancini, Jay D. (American Physical Society, 1984-08)
A convergent method of approximating thermodynamic Green functions is outlined briefly. The method constructs a sequence of approximants which converges independently of the strength of the Hamiltonian's coupling constants. Two new concepts associated with the approximants are introduced: the resolving power of the approximation, and conditional creation (annihilation) operators. These ideas are illustrated on an exactly soluble model and a numerical example. A convergent expression for the scattering rate in a field theory is also derived.
The diagramatical solution of the two-impurity Kondo problem
Zhou, Chen (Virginia Polytechnic Institute and State University, 1988)
The problem of the two-impurity Kondo problem is studied via the perturbative diagrammatical method. The high-temperature magnetic susceptibility is calculated to fourth order in the coupling constant J for different regimes. The integral equations for the ground state energy are established and solved numerically. The two-stage Kondo effect and corresponding energy scales are found which agree with the scaling results.
Explicitly structured physics instruction
Wright, David Shaw (Virginia Polytechnic Institute and State University, 1984)
In an introductory physics course, problem solving skills are not traditionally taught. The instructor explains the physical theory and works example problems. Many students, however, are not able to develop the ability to solve problems implicitly. The program of Explicitly Structured Physics Instruction (ESPI) was developed to teach problem solving skills explicitly. It is designed to help students organize their work, increase their accuracy, eliminate initial panic or lack of direction in approaching a problem, increase confidence in problem solving, promote understanding instead of rote memory, and improve the students' ability to communicate with the instructor and other students. It provides not only an explicit strategy for problem solving, but also a structure for examining formulas called the formula fact sheet, and an opportunity for practice and feedback in a problem solving session which involves the use of out loud thinking. The program of ESPI was developed over five academic quarters of testing. A statistical analysis was performed on the data obtained, but the qualitative data obtained from student interviews and questionnaires, as well as the instructor reaction to the program, provided the main source of input in the development of the program and the measurement of its success. Reaction to the program in its final revised form was very positive. Over 90% said that they would use the strategy even if it were not required, and that the formula fact sheet had been very helpful. Over 75% said that the problem solving session was very helpful. Final grades of those who used the strategy were significantly higher than those who did not. Retention of students in the course was raised from 70% to 86%. The study indicates that a well integrated program built around the use of a problem solving strategy can help students focus on understanding physics and the problem sovling process.
Finite-basis many-electron approximation to the Anderson model
Mancini, Jay D.; Bowen, Samuel P.; Zhou, Yu (American Physical Society, 1990-03)
A relatively simple many-electron basis is used to construct a matrix for the Anderson impurity Hamiltonian. The basis states are each valid in the thermodynamic limit. The approximate ground-state energy compares well with Bethe-ansatz results for large Coulomb energies. The ground-state wave-function properties are not as well approximated. This method may be well suited to studies of more realistic Hamiltonians and their ground-state energy and its derivatives.
Home energy cost-cutting computer analysis
Bowen, Samuel P.; McAnge, Thomas R. (Virginia Cooperative Extension Service, 1981-03)
A form for a free computer service that provides an estimate of heating and cooling losses in your home, and recommendations for reducing these losses.
Impulse electrical breakdown of high-purity water
Gehman, Victor H. (Virginia Tech, 1995-05-05)
Experiments have been conducted on the electrical breakdown of high-purity water and water mixtures. The electrical regime of interest has been carefully defined and documented to consist of electrical impulses with approximately microsecond rise time and fall time greater than 65 microseconds, on approximately 81-square-centimeter-area planar electrodes with a dielectric gap of approximately one centimeter. The results of over 25,000 shots by a Marx generator have been distilled into database form in an Excel spreadsheet and analysis performed to try to find patterns or indirect evidence into the nature of the breakdown-initiation process. An extensive review of all the experiments, which had been conducted over eight years by the Naval Surface Warfare Center and which had been designed to find the largest water-breakdown fields, was conducted with the intention of delineating the physical factors that led to breakdown. A variety of theoretical models of breakdown initiation were compared to the data, until it became clear that many of the breakdowns were dominated by impurities of various sorts. An extensive study of old and new experiments led to a more detailed understanding of the phenomenology of impurity-dominated water breakdown (such as the process of "conditioning" the electrodes and hysteresis) and the proposal of a number of new experiments to further characterize the intrinsic role of electrode materials on determining high-electric-field dielectric breakdown in water.
Liouville resolvent methods applied to highly correlated systems
Holtz, Susan Lady (Virginia Polytechnic Institute and State University, 1986)
In this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm.
Multigroup transport equations with nondiagonal cross section matrices
Willis, Barton L. (Virginia Polytechnic Institute and State University, 1985)
It is shown that multigroup transport equations with nondiagonal cross section matrices arise when the modal approximation is applied to energy dependent transport equations. This work is a study of such equations for the case that the cross section matrix is nondiagonalizable. For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions.
Phase transitions in thin iron-palladium films
Mattozzi, Raymond William (Virginia Polytechnic Institute and State University, 1982)
Sputtered thin films have the capability of producing a very random distribution of alloying elements within a host element. This study demonstrates the ability of the SQUID (Superconducting Quantum Undulating Interference Device) to measure the Curie temperature of thin films of Pd(1-x)Fe(x). The Curie temperatures of these films were found to be significantly less than bulk samples having the same iron concentration. The Curie temperature, furthermore, showed a systematic shift to higher values as the thickness of the film increased. Magnetic structure below the Curie temperature is revealed in magnetization and a.c. susceptibility curves for x=. 078. For other samples susceptibility data exhibited more sensitivity than magnetization in revealing magnetic detail below the Curie temperature. We attribute some of this magnetic detail to cluster glass behavior.
The role of coulomb interactions in valence transition: Falicov_Kimball model
Bowen, Samuel P.; Lady, S. C. (American Institute of Physics, 1984)
A nonperturbative method of Green function calculation is applied to the Falicov_Kimball model Hamiltonian. In an approximation to first order in the hopping matrix elements, self_consistent solutions for several thermal averages and correlation functions do not show abrupt phase changes as a function of temperature. This treatment suggests that the Coulomb correlation by itself is not the key ingredient to understanding valence transitions.
A statistical theory of the epilepsies
Thomas, Kuryan (Virginia Polytechnic Institute and State University, 1988)
A new physical and mathematical model for the epilepsies is proposed, based on the theory of bond percolation on finite lattices. Within this model, the onset of seizures in the brain is identified with the appearance of spanning clusters of neurons engaged in the spurious and uncontrollable electrical activity characteristic of seizures. It is proposed that the fraction of excitatory to inhibitory synapses can be identified with a bond probability, and that the bond probability is a randomly varying quantity displaying Gaussian statistics. The consequences of the proposed model to the treatment of the epilepsies is explored. The nature of the data on the epilepsies which can be acquired in a clinical setting is described. It is shown that such data can be analyzed to provide preliminary support for the bond percolation hypothesis, and to quantify the efficacy of anti-epileptic drugs in a treatment program. The results of a battery of statistical tests on seizure distributions are discussed. The physical theory of the electroencephalogram (EEG) is described, and extant models of the electrical activity measured by the EEG are discussed, with an emphasis on their physical behavior. A proposal is made to explain the difference between the power spectra of electrical activity measured with cranial probes and with the EEG. Statistical tests on the characteristic EEG manifestations of epileptic activity are conducted, and their results described. Computer simulations of a correlated bond percolating system are constructed. It is shown that the statistical properties of the results of such a simulation are strongly suggestive of the statistical properties of clinical data. The study finds no contradictions between the predictions of the bond percolation model and the observed properties of the available data. Suggestions are made for further research and for techniques based on the proposed model which may be used for tuning the effects of anti-epileptic drugs.
Strongly correlated electron ground_state energy approximations for Anderson_like models
Mancini, Jay D.; Potter, Charles D.; Bowen, Samuel P. (American Institute of Physics, 1987-04-15)
We report preliminary results of convergence properties for nonperturbative resolvent approximations to Anderson_like models of magnetic ions in metals. Our study is initially focused on the spin_ 1/2 Anderson model for magnetic impurities, but the methods studied can include multiplet and crystal_field effects which are needed for more accurate descriptions of real systems. We will compare the nonperturbative Lanczos method (tridiagonalization) and similar truncation schemes to exact ground_state energies for the impurity model and assess the efficacy of these nonperturbative approaches to understanding the Anderson lattice, heavy fermions, and other strongly interacting electronic systems.
The study of many-electron systems
Zhou, Yu (Virginia Tech, 1991)
Various methods and approximation schemes are used to study many-electron interacting systems. Two important many-particle models, the Anderson model and the Hubbard model, and their electromagnetic properties have been investigated in many parameter regimes, and applied to physical systems. An Anderson single-impurity model Hamiltonian based calculation of the magnetic susceptibility is performed for YbN in the presence of crystal fields using an alteration of the Non-Crossing Approximation proposed by Zwicknagl et.al., incorporating parameters obtained from ab initio band structure calculations. It yields good agreement with experimental data. For the Anderson lattice model, a variational scheme which uses specific many-electron wavefunctions as basis is applied to both one- and two-dimensional systems represented by symmetric Anderson lattice Hamiltonians. Without much computational effort, the ground state energy is well approximated, especially in strong-coupling limit. Some electronic properties are examined using the variational ground state wavefunction. The one-dimensional Hubbard model has been solved exactly for small-size clusters by diagonalizing the Hamiltonian in the basis of many-electron Bloch states. The results for the energy spectrum and eigenfunctions of the ground state and low-lying excited states are presented. Also, mean field calculations of the two-dimensional single-band Hubbard model and Cu-O lattice model (three-band Hubbard model) are carried out for various physical quantities including the energy, occupation probability, staggered magnetization, momentum distribution Fermi surface and density of states, by using a projection operator formalism. To develop a systematic approach to solving many-electron problems, the many-particle partition function for the free electron gas system is explored using a cumulant expansion scheme. Starting from the ground state, the partition function can be approximated to any order in terms of excitation energy. Its application to interacting systems such as the Anderson model and the Hubbard model is briefly discussed.
Variational ground state for the periodic Anderson model
Bowen, Samuel P.; Mancini, Jay D. (American Institute of Physics, 1988-04-15)
A variational calculation of the ground state of the Anderson lattice model is discussed. The calculation creates a finite Hamiltonian matrix for many_electron states, which are appropriate for the thermodynamic limit. A simple 14_14 truncation is discussed for finite U and a smaller 3_3 is used for the large U limit. Both approximations indicate that the spin configurations of the localized f orbitals are antiferromagnetically correlated for nearest neighbors in the ground state. This antiferromagnetic correlation is mediated by an RKKY interaction and thus offers a variety of spin orderings as a function of lattice and density.

Browsing by Author "Bowen, Samuel P."

Results Per Page

Sort Options