Dynamical localization, measurements and quantum computing

We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability spreading, our results demonstrate that localization can be preserved for repeated single-qubit measurements. We detect a transition from a localized to a delocalized phase, depending on the system parameters and on the choice of the measured qubit.Comment: 4 pages, 4 figures, research at Quantware MIPS Center http://www.quantware.ups-tlse.f

Chaos, Fractals and Inflation

In order to draw out the essential behavior of the universe, investigations of early universe cosmology often reduce the complex system to a simple integrable system. Inflationary models are of this kind as they focus on simple scalar field scenarios with correspondingly simple dynamics. However, we can be assured that the universe is crowded with many interacting fields of which the inflaton is but one. As we describe, the nonlinear nature of these interactions can result in a complex, chaotic evolution of the universe. Here we illustrate how chaotic effects can arise even in basic models such as homogeneous, isotropic universes with two scalar fields. We find inflating universes which act as attractors in the space of initial conditions. These universes display chaotic transients in their early evolution. The chaotic character is reflected by the fractal border to the basin of attraction. The broader implications are likely to be felt in the process of reheating as well as in the nature of the cosmic background radiation.Comment: 16 pages, RevTeX. See published version for fig

Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain

We study numerically and analytically the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations which are exponentially close to the energy of the ground state. The energies of these configurations form a fractal quasi-degenerate band structure which is described on the basis of elementary excitations. Contrary to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure

Dynamics of some piecewise smooth Fermi-Ulam Models

We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first case we prove that the set of orbits undergoing Fermi acceleration has zero measure but full Hausdorff dimension. We also show that for almost every orbit the energy eventually falls below a fixed threshold. In the second case we prove that, generically, we have stable periodic orbits for arbitrarily high energies, and that the set of Fermi accelerating orbits may have infinite measure.Comment: 22 pages, 4 figure