Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version is shortened and the arguments streamlined. Minor changes in notation and figures. This version matches the published versio

Quantum matchgate computations and linear threshold gates

The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

Fluoride-containing bioactive glasses: Effect of glass design and structure on degradation, pH and apatite formation in simulated body fluid

NOTICE: this is the author’s version of a work that was accepted for publication in Acta Biomaterialia. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Acta Biomaterialia, [VOL 6, ISSUE 8, (2010)] DOI: 10.1016/j.actbio.2010.01.04

Generalized Satisfiability Problems via Operator Assignments

Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in which the Fourier transform is used to represent constraints by multilinear polynomials in a unique way. The polynomial representation of constraints gives rise to a relaxation of the notion of satisfiability in which the values to variables are linear operators on some Hilbert space. For the case of constraints given by a system of linear equations over the two-element field, this relaxation has received considerable attention in the foundations of quantum mechanics, where such constructions as the Mermin-Peres magic square show that there are systems that have no solutions in the Boolean domain, but have solutions via operator assignments on some finite-dimensional Hilbert space. We obtain a complete characterization of the classes of Boolean relations for which there is a gap between satisfiability in the Boolean domain and the relaxation of satisfiability via operator assignments. To establish our main result, we adapt the notion of primitive-positive definability (pp-definability) to our setting, a notion that has been used extensively in the study of constraint satisfaction problems. Here, we show that pp-definability gives rise to gadget reductions that preserve satisfiability gaps. We also present several additional applications of this method. In particular and perhaps surprisingly, we show that the relaxed notion of pp-definability in which the quantified variables are allowed to range over operator assignments gives no additional expressive power in defining Boolean relations

Neutrinoless Double Beta Decay and CP Violation

We study the relation between the Majorana neutrino mass matrices and the neutrinoless double beta decay when CP is not conserved. We give an explicit form of the decay rate in terms of a rephasing invariant quantity and demonstrate that in the presence of CP violation it is impossible to have vanishing neutrinoless double beta decay in the case of two neutrino generations (or when the third generation leptons do not mix with other leptons and hence decouple).Comment: 9 pages, UTPT-93-1

The exclusive \bar{B} --> \pi e^+ e^- and \bar{B} --> \rho e^+ e^- decays in the two Higgs doublet model with flavor changing neutral currents

We calculate the leading logarithmic QCD corrections to the matrix element of the decay b --> d e^+ e^- in the two Higgs doublet model with tree level flavor changing currents (model III). We continue studying the differential branching ratio and the CP violating asymmetry for the exclusive decays B --> \pi e^+ e^- and B --> \rho e^+ e^- and analysing the dependencies of these quantities on the selected model III parameters, \xi^{U,D}, including the leading logarithmic QCD corrections. Further, we present the forward-backward asymmetry of dileptons for the decay B --> \rho e^+ e^- and discuss the dependencies to the model III parameters. We observe that there is a possibility to enhance the branching ratios and suppress the CP violating effects for both decays in the framework of the model III. Therefore, the measurements of these quantities will be an efficient tool to search the new physics beyond the SM.Comment: 27 pages, 14 Figure

Non-Statistical Effects in Neutron Capture

There have been many reports of non-statistical effects in neutron-capture measurements. However, reports of deviations of reduced-neutron-width distributions from the expected Porter-Thomas (PT) shape largely have been ignored. Most of these deviations have been reported for odd-A nuclides. Because reliable spin (J) assignments have been absent for most resonances for such nuclides, it is possible that reported deviations from PT might be due to incorrect J assignments. We recently developed a new method for measuring spins of neutron resonances by using the DANCE detector at LANSCE. Measurements made with a 147Sm sample allowed us to determine spins of almost all known resonances below 1 keV. Furthermore, analysis of these data revealed that the reduced-neutron-width distribution was in good agreement with PT for resonances below 350 eV, but in disagreement with PT for resonances between 350 and 700 eV. Our previous (n,alpha) measurements had revealed that the alpha strength function also changes abruptly at this energy. There currently is no known explanation for these two non-statistical effects. Recently, we have developed another new method for determining the spins of neutron resonances. To implement this technique required a small change (to record pulse-height information for coincidence events) to a much simpler apparatus: A pair of C6D6 gamma-ray detectors which we have employed for many years to measure neutron-capture cross sections at ORELA. Measurements with a 95Mo sample revealed that not only does the method work very well for determining spins, but it also makes possible parity assignments. Taken together, these new techniques at LANSCE and ORELA could be very useful for further elucidation of non-statistical effects.Comment: 8 pages, 3 figures, for proceedings of CGS1

B -> K^* gamma from D -> K^* l nu

The B -> K^* gamma branching fraction is predicted using heavy quark spin symmetry at large recoil to relate the tensor and (axial-)vector form factors, using heavy quark flavor symmetry to relate the B decay form factors to the measured D -> K^* l nu form form factors, and extrapolating the semileptonic B decay form factors to large recoil assuming nearest pole dominance. This prediction agrees with data surprisingly well, and we comment on its implications for the extraction of |Vub| from B -> rho l nu.Comment: 10 page

Thermodynamic metrics and optimal paths

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.Comment: 5 page