Samuel P. Bowen

Moments expansion study of the Rabi Hamiltonian

Abstract The interaction of a single bosonic mode with a two-level fermion system is investigated. For the condensed-matter physicist the boson in question is typically a phonon whereas the fermion system is represented by a two-level electron structure. In this work we shall use both the connected moments expansion (CMX) and the alternate moments expansion (AMX) as well as the non-perturbative Lanczos tridiagonal scheme to study the ground-state spectrum of this system. Comparisons will be made with other approximation schemes as well as “exact” methods.

Why do Electromagnetic Pulses Enhance Bone Growth

The excitation probability of substrate molecules involved in the production of growth factors influencing the division of chondrocytes in the growth layer of bone under the influence of pulsed electromagnetic fields is studied theoretically in a quantum mechanical model calculation. In this model matrix elements and anti-bonding energy levels are assumed known and the dynamics of the interaction with pulsed electromagnetic fields is derived. The derivation makes it clear that continuous pulsing or large driving currents can overwhelm local diffusive transport to the growth plane resulting in a loss of its enhancement properties. Optimal locations within a pair of Helmholtz coils for enhancement of bone growth are also investigated and found to be close to the coils. The work presented here is believed to be the first derivation in a model calculation of a physical basis for the effects of pulsed electromagnetic fields on bone growth and fusion.

Using the resources of the student at the urban, comprehensive university to develop an effective instructional environment

Physics Education Researchers have provided instructors with (1) tools to assess student learning, (2) details on the state of student knowledge, and (3) instructional materials and learning environments that have proven to be effective in promoting understanding. Unfortunately, the vast majority of this work has centered on students and instruction at the traditional research university. As instructors begin to implement innovative instructional materials, and as researchers begin to investigate student learning with diverse populations, complex differences emerge. The use of traditional PER tools in non‐traditional environments, such as the urban, comprehensive university, often leads to a very narrow picture of student development. Often, this limited view highlights deficiencies in learning and fails to reveal the strengths and resources of this population. In this paper we highlight issues we face with some of the traditional research tools and provide evidence for the resources we have found with ou...

Freeman Dyson was right about analyticity and perturbation series

Here we wish to study the exact eigenvalues of a family of one-dimensional, positive, symmetric potentials with two turning points, which includes the simple harmonic oscillator. The eigenvalues are shown to depend on branch point singularities in the coupling constant by both Bohr–Sommerfeld and canonical quantization procedures, thus ruling out convergent power series expansions in the coupling constant and severely restricting the analytic continuation of the coupling constant g in the complex plane. In particular, analytic continuation of the eigenvalues from positive to negative values in the usual inertial Hilbert space is not possible because of the branch point singularities as Dyson argued long ago.

An improved systematic variational method: application to a nuclear system

Abstract A recently developed scheme for generating a variational set of basis states is applied to the determination of the binding energy of a deuteron nucleus. The method has the advantage of being a single-parameter theory which is systematic, and hence, straightforward to generate. Convergence is rapid and the exact (experimental) binding energy is obtained after just five iterations.

Moments expansions for the correlation energy of an exactly solvable problem

In this work we study the ground-state properties of the model Hamiltonian , which represents a set of N one-dimensional correlated harmonic oscillators. Here the parameter g describes the coupling between oscillators and may be either real (attractive case) or purely imaginary (repulsive case). We wish to study the correlation energy of the system by two methods: the Lanczos tridiagonal scheme and a newly developed moments expansion AMX (alternate moments expansion). Comparisons will be made with other moments expansions, in particular the CMX−LT(2) and CMX−LT(3) series.

Ground-state of the single impurity Anderson model with correlated conduction electrons

Utilizing the nonperturbative Lanczos procedure, we study the ground-state spectrum of the Single-Impurity Anderson Model. An additional term is added to the Hamiltonian which represents a Coulomb-repulsion between the conduction electrons. The ground-state energy as well as the singlet-triplet energy is calculated in this strongly interacting system. Our results are consistent with those of Fermi-liquid theory which predicts a renormalization of the low energy properties of the system upon introduction of local, repulsive conduction electron interactions.