Existence of Dirac resonances in the semi-classical limit

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials V decaying like ⟨x⟩−δ at infinity for some δ>0. By studying analytic singularities of a certain distribution related to V and by combining two trace formulas, we prove that the perturbed Dirac operators possess resonances near supV+1 and infV−1. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter

Existence of a minimizer for the quasi-relativistic Kohn-Sham model

We study the standard and extended Kohn-Sham models for quasi-relativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator $$sqrt{-alpha^{-2}Delta_{x_n}+alpha^{-4}}-alpha^{-2}.$$ For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge $Z_{m tot}$ of K nuclei is greater than N-1 and that $Z_{m tot}$ is smaller than a critical charge $Z_{m c}=2 alpha^{-1} pi^{-1}$

Cryogenic optical refrigeration: Laser cooling of solids below 123 K

This dissertation compiles recent achievements in optical refrigeration, cooling a 10% wt. Ytterbium doped Yttrium Lithium Fluoride (Yb+3:YLF) crystal via anti-Stokes fluorescence to a record low temperature ~114(+\\-1)K (below NIST-defined cryogenic 123 K) from room temperature (ΔT ~185 K) in a single stage with a cooling power of 190mW. The demonstration of the coldest temperature to date, without the use of liquid cryogens or mechanical refrigerators, is achieved by taking advantage of the Stark manifold resonance and high doping concentration available in a crystalline host, outperforming multi-stage Peltier coolers. A novel technique probing local temperature changes experimentally verifies the cooling efficiency model with expected cooling to 93 K with the current crystal. With modest improvements to parasitic background absorption through the reduction of identified impurities, theory predicts cooling that approaches liquid nitrogen temperatures at 77 K. With this accomplishment, implementation of all solid-state cryo-cooling has begun

Effects of wastewater on fish and macroinvertebrates of selected small East Tennessee streams

This study Investigated the impacts of several municipal and industrial wastewater discharges on the aquatic fauna of four small east Tennessee streams. Water samples were collected at 13 locations and analyzed for 25 chemical parameters. Aquatic macroinvertebrates and fish were collected quantitatively and qualitatively at the same 13 sample stations. The data were used to determine if damage had occurred to the aquatic communities and, if so, to determine the specific cause of the damage. The results indicated severe impacts to the fish and macroinvertebrate communities existed downstream of most of the effluent discharge points. In some cases, copper, zinc, or lead appeared to be the cause of the ecosystem degradation; in other cases, ammonia and chlorine toxicity seemed to cause the damage. Closer scrutiny of effluent constituents and toxicity is cited as a need to better protect the aquatic fauna of small streams that receive large amounts of complex industrial and municipal wastes