Jay D. Mancini

Microseism and infrasound generation by cyclones

A two-dimensional cylindrical shear-flow wave theory for the generation of microseisms and infrasound by hurricanes and cyclones is developed as a linearized theory paralleling the seminal work by Longuet-Higgins which was limited to one-dimensional plane waves. Both theories are based on Bernoullis principle. A little appreciated consequence of the Bernoulli principle is that surface gravity waves induce a time dependent pressure on the sea floor through a vertical column of water. A significant difference exists between microseisms detected at the bottom of each column and seismic signals radiated into the crust through coherence over a region of the sea floor. The dominant measured frequency of radiated microseisms is matched by this new theory for seismic data gathered at the Fordham Seismic Station both for a hurricane and a mid-latitude cyclone in 1998. Implications for Bernoullis principle and this cylindrical stress flow theory on observations in the literature are also discussed.

Ground-state energy of the Wolff model

Abstract Using the connected moments expansions (CMX) to third order, we have evaluated the ground-state energy of the single-impurity Wolff model. Comparisons are made with an equivalent Lanczos tridiagonalization truncation as well as second-order perturbation theory. All ranges of parameter space are considered with an isolated singularity arising in the CMX expansion.

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.

ENERGY EIGENSTATES IN A STATIC SCREENED COULOMB POTENTIAL

Abstract A recently developed variational scheme is applied to the calculation of the ground-state and excited-state energies of an electron bound in a screened Coulomb potential. A basis of independent functions is generated by expanding an initial trial wavefunction around a variational parameter. The calculated eigenenergies are compared with other variational methods and the exact results.

Comparison between Lanczos and linked cluster methods for the Heisenberg antiferromagnet on a square lattice

The Lanczos tridiagonal scheme is applied to investigate the ground-state energy of the 2D anisotropic XXZ Heisenberg Model. Comparisons are made with connected moments and t-expansion methods as well as a recently deveoped plaquette expansion. A number of poles appear in each of the schemes, which has previously been unreported.

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.

NUMERICAL SINGULARITIES IN MANY-BODY MOMENTS EXPANSIONS

Abstract It is well known that connected moments expansions when used to approximate the ground-state energy of Hamiltonian systems may suffer from extraneous singularities in various regions of parameter space. In this brief Letter a numerical investigation is presented to study an approximation scheme developed by Ullah to avoid the singularities found in moments expansions. Specifically, we study the single-impurity Wolff model as well as the 32-site Anderson lattice.

Coupling of N -quantum-wire plasmons with surface and bulk collective modes of the host semiconductor

Abstract We have examined the dynamic dielectric response properties of a multiple quantum-wire system embedded in a semi-infinite plasma-like host medium assuming that each wire has just one active subband. The geometric dependence on z0, the distance of the first quantum-wire from the bounding surface is determined. In particular, the coupled mode dispersion relation for the plasmons of an N-quantum-wire system in interaction with the surface and bulk plasmons of the host material is analyzed and its dependence on z0 is exhibited.

Avoidance of singularities in moments expansions: a numerical study

Abstract The use of connected moments expansions to approximate the ground-state energy of many-body systems is well-known to suffer from extraneous singularities throughout parameter space. Recently Ullah has derived an approximation based on a probability distribution function having a delta-function and a uniform distribution. The expressions obtained up to second order do not have the singularities which plague the connected moments expansions. In this paper, we apply the approximation of Ullah to the harmonic oscillator, the anharmonic oscillator and the Kondo Hamiltonian.

Ground-state of the linear anisotropic antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions

Abstract Using a modified Lanczos scheme, we evaluate the ground state properties of a sixteen-site one-dimensional spin- 1 2 Heisenberg antiferromagnet. We consider the case with nearest-neighbor antiferromagnetic interactions and next-nearest-neighbor ferromagnetic interactions as well as anisotropy. Comparisons are made with other exact results in the appropriate regions of parameter space.