D-particle bound states and generalized instantons

We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of $\mathcal{N}=1$, $D=4,6,10$ super-Yang-Mills theories with gauge group SU(N). The results are: ${1\over{N^{2}}}$ for $D=4,6$, $\sum_{d | N} {1\over{d^{2}}}$ for D=10. We also discuss the D=3 case.Comment: harvmac, 24 pages; v2. references added, typos corrected; v3. one more reference adde

Integrating Over Higgs Branches

We develop some useful techinques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkahler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkahler periods. We also reduce these volumes for a large class of hyperkahler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on R^4 and ALE manifolds, Hitchin spaces, and moduli spaces of parabolic Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe Ansatz equations for the non-linear Schroedinger system. We discuss some applications of our results.Comment: 32pp. harvmac big mode; v.2 34pp. typos fixed, sections 4.1, 5.2 substantially improve

Theory and application of Fermi pseudo-potential in one dimension

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer.Comment: RevTeX4, 32 pages, no figure

The Semiclassical and Quantum Regimes of Superradiant Light Scattering from a Bose-Einstein Condensate

We show that many features of the recent experiments of Schneble et al. [D. Schneble, Y. Torii, M. Boyd, E.W. Streed, D.E. Pritchard and W. Ketterle, Science vol. 300, p. 475 (2003)], which demonstrate two different regimes of light scattering by a Bose-Einstein condensate, can be described using a one-dimensional mean-field quantum CARL model, where optical amplification occurs simultaneously with the production of a periodic density modulation in the atomic medium. The two regimes of light scattering observed in these experiments, originally described as ``Kapiza-Dirac scattering'' and ``Superradiant Rayleigh scattering'', can be interpreted as the semiclassical and quantum limits respectively of CARL lasing.Comment: 10 pages, 5 figures - to appear in Journal of Optics

Monte Carlo Evaluation of Non-Abelian Statistics

We develop a general framework to (numerically) study adiabatic braiding of quasiholes in fractional quantum Hall systems. Specifically, we investigate the Moore-Read (MR) state at $\nu=1/2$ filling factor, a known candidate for non-Abelian statistics, which appears to actually occur in nature. The non-Abelian statistics of MR quasiholes is demonstrated explicitly for the first time, confirming the results predicted by conformal field theories.Comment: 4 pages, 4 figure

Fractional quantum Hall effect and nonabelian statistics

It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The Pfaffian state is related to the 2D Ising model and possesses fractionally charged excitations which are predicted to obey nonabelian statistics

The Rhodium Less Travelled: Understanding the Influence of Bipyridyl Ligand Substituents on [Cp*Rh] Catalysts for Hydrogen Evolution

This undergraduate thesis was submitted to the Faculty of the Department of Chemistry in Partial Fulfillment of the Requirements for Departmental Honors in ChemistryThis thesis details a two-part investigation into the [Cp*Rh(bpy)] framework (where Cp* = pentamethylcyclopentadienyl and bpy = 2,2'-bipyridyl), a known platform for electrocatalytically generating hydrogen. Chapter 1 of this thesis describes an in-depth investigation into the characteristics of a [Cp*Rh] complex (1) bearing the 4,4´-dinitro-2,2´-bipyridyl (4,4´-NO2bpy) ligand and multiple reduced forms of 1. Isolated 1 was characterized by several forms of spectroscopy including nuclear magnetic resonance, electronic absorption, and mass spectrometry. Moreover, single crystals suitable for X-ray diffraction analysis were grown, and the structure of 1 solved with the help of Dr. Victor W. Day. Electrochemical studies reveal that 1 is the first example of a monometallic [Cp*Rh] complex that exhibits three quasi-reversible one-electron reductions and a fourth irreversible reduction. In these studies, a rather large spacing between the redox events (~ 0.5 V) suggested the possibility of isolating one or more of the reduced species. In accord with this theory, the singly reduced species (2) could be chemically prepared and isolated. UV-visible absorption spectra display new peaks that correspond to the readily observed color change from red/orange to green upon reduction of 1 to 2. X-band electron paramagnetic resonance spectroscopy confirms the paramagnetic nature of 2, and reveals a narrow signal at g = 2.006, consistent with the majority of the unpaired electron density being localized on the 4,4´-NO2bpy ligand. Cyclic voltammetry and spectroelectrochemistry further confirm that 2 is produced by both electrochemical and chemical reduction of 1, and that the second reduction of 1 is primarily metal-centered. Electrocatalytic studies reveal that the extremely electron-withdrawing nature of the nitro substituents effectively eliminates catalytic function, providing insight into the features that govern catalysis in [Cp*Rh] complexes. Chapter 2 describes investigations of a second less-studied aspect of the [Cp*Rh(bpy)] framework: namely, the role of less symmetric substitution of the bipyridyl ligand in modulating reduction potentials and catalytic competence. In this work, a new divergent synthetic route was developed, in which known synthetic steps were strategically assembled to provide straightforward access to a small family of [Cp*Rh] complexes bearing a single substituent at the 4-position of the bpy ligand. The method thus developed enabled preparation of three new C1-symmetric complexes with different substitutions at the 4 position of one of the pyridine rings of the bpy ligand: –NO2 (3), –Cl (4), or –NH2 (6). NMR spectroscopic characterization supports successful formation of the new diamagnetic compounds. Hammett analysis reveals a dependence of intraligand charge transfer (ILCT) energy and metal-to-ligand or ligand-to-metal charge transfer (MLCT or LMCT) energy on the bpy ligand substituents, as reported by use of the σp+ parameter. Electrochemical studies also confirm a Hammett parameter dependence of the reduction potentials of the new compounds, confirming an important role for singly substituted bipyridyl-type ligands in influencing the electrochemical behavior of [Cp*Rh(bpy)]-type complexes. Specifically, the more electron-donating substituents (as judged via the σp– parameter) are associated with complexes displaying more negative reduction potentials. Building on the findings from Chapter 1, cyclic voltammograms collected with complex 3, bearing the 4-nitro-2,2´-bipyridyl ligand, reveal slow chloride ligand loss upon one-electron reduction, implicating significant stabilization of the singly-reduced form by the single electron-withdrawing nitro group. As the chemical and electrochemical properties of these complexes are readily modulated by substituent effects, the strategy of ligand modification can thus be realistically anticipated to afford fine-grained control of electrocatalysis in future studies

Confinement-induced Berry phase and helicity-dependent photocurrents

The photocurrent in an optically active metal is known to contain a component that switches sign with the helicity of the incident radiation. At low frequencies, this current depends on the orbital Berry phase of the Bloch electrons via the "anomalous velocity" of Karplus and Luttinger. We consider quantum wells in which the parent material, such as GaAs, is not optically active and the relevant Berry phase only arises as a result of quantum confinement. Using an envelope approximation that is supported by numerical tight-binding results, it is shown that the Berry phase contribution is determined for realistic wells by a cubic Berry phase intrinsic to the bulk material, the well width, and the well direction. These results for the magnitude of the Berry-phase effect suggest that it may already have been observed in quantum well experiments.Comment: 4 pages, 2 figure

Implicit Simulations using Messaging Protocols

A novel algorithm for performing parallel, distributed computer simulations on the Internet using IP control messages is introduced. The algorithm employs carefully constructed ICMP packets which enable the required computations to be completed as part of the standard IP communication protocol. After providing a detailed description of the algorithm, experimental applications in the areas of stochastic neural networks and deterministic cellular automata are discussed. As an example of the algorithms potential power, a simulation of a deterministic cellular automaton involving 10^5 Internet connected devices was performed.Comment: 14 pages, 3 figure

Coherent phonon scattering effects on thermal transport in thin semiconductor nanowires

The thermal conductance by phonons of a quasi-one-dimensional solid with isotope or defect scattering is studied using the Landauer formalism for thermal transport. The conductance shows a crossover from localized to Ohmic behavior, just as for electrons, but the nature of this crossover is modified by delocalization of phonons at low frequency. A scalable numerical transfer-matrix technique is developed and applied to model quasi-one-dimensional systems in order to confirm simple analytic predictions. We argue that existing thermal conductivity data on semiconductor nanowires, showing an unexpected linear dependence, can be understood through a model that combines incoherent surface scattering for short-wavelength phonons with nearly ballistic long-wavelength phonons. It is also found that even when strong phonon localization effects would be observed if defects are distributed throughout the wire, localization effects are much weaker when defects are localized at the boundary, as in current experiments.Comment: 13 page