An equation for the description of volume and temperature dependences of the dynamics of supercooled liquids and polymer melts

A recently proposed expression to describe the temperature and volume dependences of the structural (or alpha) relaxation time is discussed. This equation satisfies the scaling law for the relaxation times, tau = f(TV^g), where T is temperature, V the specific volume, and g a material-dependent constant. The expression for the function f is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover, providing a description of the dynamics with a minimal number of parameters. The results herein can be reconciled with previously found correlations of the isochoric fragility with both the isobaric fragility at atmospheric pressure and the scaling exponent g.Comment: to be published in the special edition of J. Non-Crystalline Solids honoring K.L. Nga

Quantum circuit implementation of the Hamiltonian versions of Grover's algorithm

We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely related algorithms in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This make it possible to implement the last two algorithms by Hamiltonian evolution on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm.Comment: 5 pages, 3 figure

Time domain calculation of the electromagnetic self-force on eccentric geodesics in Schwarzschild spacetime

I calculate the self-force acting on a particle with electric charge q moving on a generic geodesic around a Schwarzschild black hole. Using methods similar to those developed for the scalar field case discussed in a previous paper, I investigate the relative sizes of the conservative (half-advanced plus half-retarded) and dissipative (half-advanced minus half-retarded) pieces of the self-force. I also display the regularization parameters used in the mode-sum regularization scheme.Comment: 24 pages; 21 figures; revtex

Ray class fields of global function fields with many rational places

A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.Comment: Latex2e, 27 pages, 20 tables, revised version as submitted to Acta Arithmetic