Related papers: Phase space analysis of higher-order dispersive eq…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Long-term quantum coherence constitutes one of the main challenges when engineering quantum devices. However, easily accessible means to quantify complex decoherence mechanisms are not readily available, nor are sufficiently stable systems.…
The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
In this paper the interaction of a scalar field and the electromagnetic field in phase space is analyzed. The scattering process is calculated up to first order in the Planck constant which is obtained by an expansion of the Moyal product…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
We develop a non-Gaussian variational approach that enables us to study both equilibrium and far-from-equilibrium physics of the two-dimensional Fermi polaron. This method provides an unbiased analysis of the polaron-to-molecule phase…
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a…
We present the applications of nonlinear local harmonic analysis methods to the modelling of beam-beam interaction. Our approach is based on methods provided the possibility to work with dynamical beam localization in phase space. The…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
We investigate the case of phase-matched high-harmonic generation in a gas-filled capillary waveguide, comparing in detail theory with experiment. We observe three different regimes of phase matching: one where atomic dispersion balances…
We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is…
Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in…