Related papers: Noncommuting vector fields, polynomial approximati…
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
\noindent In our contribution to this volume we deal with \emph{discrete} symmetries: these are symmetries based upon groups with a discrete set of elements (generally a set of elements that can be enumerated by the positive integers). In…
These notes provide a pedagogical introduction to the theoretical study of vacuum polarization effects in strong electromagnetic fields as provided by state-of-the-art high-intensity lasers. Quantum vacuum fluctuations give rise to…
We analyze some specific features of the beam-plasma instability. In particular, non-perturbative effects in the dispersion relation are studied when the standard perturbative inverse Landau damping treatment breaks down. We also elucidate…
Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual…
We present a technique, {\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
We study the dynamics of multipulse solutions in mode-locked lasers in presence of time-delayed feedback stemming, e.g., from reflections upon optical elements, and carrier dynamics. We demonstrate that the dynamics of such a high…
Nonlinear phenomena and turbulence are central to our understanding and modeling the dynamics of fluids and plasmas, and yet they still resist analytical resolutions in many instances. However, progress has been made recently, displaying a…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly…
The sensitivity of quantum magnetometers is challenged by control errors and, especially in the solid-state, by their short coherence times. Refocusing techniques can overcome these limitations and improve the sensitivity to periodic…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We investigate theoretically and experimentally fluctuations of high spin (F>1/2) beyond the linear response regime and demonstrate dramatic modifications of the spin noise spectra in the high power density probe field. Several effects…
While thermostated time evolutions stand on firm grounds and are widely used in classical molecular dynamics (MD) simulations, similar methods for quantum MD schemes are still lacking. In the special case of a quantum particle in a harmonic…
In these pedagogical notes the diffuson-cooperon perturbation theory of weak localization and mesoscopic phenomena is extended to describe non-equilibrium and nonlinear effects in quantum disordered systems. It is shown how such…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We investigate the existence of envelope soliton solutions in collisionless quantum plasmas, using the quantum-corrected Zakharov equations in the kinetic case, which describes the interaction between high frequency Langmuir waves and low…
Measuring an observable which does not commute with the Hamiltonian of a quantum system usually modifies the mean energy of this system. In an autonomous measurement scheme, coupling the system to a quantum meter, the system's energy change…