Personal Research

In addition to contributing to my primary research responsibilities with respect to multi-disciplinary projects as part of my research associateship at the University of Texas at Dallas, I am pursuing my personal interests in theoretical and experimental research in fundamental physics.

• I have developed a fully-partitioned electrostatics interactions—discrete charge dielectric (DCD)—model, a general expression pertinent to the evaluation of the total potential energy stored in a dielectric system containing point charges (e.g. electrons). Among the many interesting features resulting from this model, I observe energy trends for spherical systems in which I conjecture the exclusion principle is exhibited as a consequence of the model rather than an a priori assumption based on empirical evidence as in most other models.

• I have derived a new expression for monophasic capacitance that is especially useful in the comprehension of electrostatic properties of few-electron systems -- particularly nanoscale systems, such as quantum dots.

• I have demonstrated a classical electrostatic "fingerprint" of the periodic table of elements. In particular, based on properties dependent on the spatial point charge symmetries given by solutions of the DCD model for electrons contrained to a dielectric sphere, a distribution (or "fingerprint") of energy differences is shown coincident with the distribution of atomic shell structure. At present, the distribution coincides well with empirical size-independent ionization energies. I am presently attempting to comprehend a manner in which size-dependence may be obtained within the classical picture.

• The classical electrostatic Thomson Problem, of uniformly distributing equal point charges on a mathematical unit sphere, lies at the heart of the classical electrostatic fingerprint of the periodic table. The fingerprint may be demonstrated independent of the DCD model, using only well-established numerical solutions of the Thomson Problem found throughout the literature.

• I have realized a particular path from which the solution of Thomson's Problem for a particular N-electron system may be obtained from a known solution for (N-1)-electron system or (N+1)-electron system. The path is two-fold, having a nonlinear term (the distribution of which I have described as the classical electrostatic fingerprint of the periodic table) and a perfectly linear term (which I might conjecture as being related to Planck's constant as the energy is linearly dependent on N).

• I have proposed a novel approach to the quantum mechanical solutions of one- and two- electrons in a spherical quantum dot by means of a dielectric framework.