Dynamics of a Classical Particle in a Quasi Periodic Potential

We study the dynamics of a one-dimensional classical particle in a space and time dependent potential with randomly chosen parameters. The focus of this work is a quasi-periodic potential, which only includes a finite number of Fourier components. The momentum is calculated analytically for short time within a self-consistent approximation, under certain conditions. We find that the dynamics can be described by a model of a random walk between the Chirikov resonances, which are resonances between the particle momentum and the Fourier components of the potential. We use numerical methods to test these results and to evaluate the important properties, such as the characteristic hopping time between the resonances. This work sheds light on the short time dynamics induced by potentials which are relevant for optics and atom optics

Asymptotically linear fractional Schrodinger equations

By exploiting a variational technique based upon projecting over the Pohozaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrodinger equations having a nonhomogenous nonautonomous asymptotically linear nonlinearity.Comment: 24 page

Phase-ordering kinetics: ageing and local scale-invariance

Dynamical scaling in ageing systems, notably in phase-ordering kinetics, is well-established. New evidence in favour of Galilei-invariance in phase-ordering kinetics is reviewed.Comment: 7 pages, 1 figure,with AIP macros, based on invited talks given at the 8th Granada Seminar on Computational and Statistical Physics (7-11 February 2005) and at the Symposium `Renormalization and Scaling' at Berlin (5th of March 2005

Grover's algorithm on a Feynman computer

We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a single, time-independent Hamiltonian. We examine issues of locality and resource usage in implementing such a Hamiltonian. In the familiar language of Heisenberg spin-spin coupling, the clocking mechanism appears as an excitation of a basically linear chain of spins, with occasional controlled jumps that allow for motion on a planar graph: in this sense our model implements the idea of "timing" a quantum algorithm using a continuous-time random walk. In this context we examine some consequences of the entanglement between the states of the input/output register and the states of the quantum clock