Related papers: Fractional quantum fields with Le'vy paths
We address the propagation of the spin along classical trajectories for a 1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities we…
An impact of integration over the paths of the Levy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox H-function. A new equation for the kernel…
A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…
Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave…
To describe the grazing scattering of keV atoms at surface, a new quantum binary collision model have been proposed where the dynamical properties of the surface atoms are considered via the wave-function of the local Debye harmonic…
The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals to the de Broglie…
We introduce and discuss the one-dimensional L\'{e}vy crystal as a probable candidate for an experimentally accessible realization of space fractional quantum mechanics (SFQM) in a condensed matter environment. The discretization of the…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
We consider the dynamics of noninteracting electrons on a square lattice in the presence of a magnetic flux {\alpha} and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics of an electron will be…
A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly…
Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It…
We study scalar field theories on Poincare invariant commutative nonassociative spacetimes. We compute the one-loop self-energy diagrams in the ordinary path integral quantization scheme with Feynman's prescription, and find that the…
Spatial spread of minority carriers produced by optical excitation in semiconductors is usually well described by a diffusion equation. The classical diffusion process can be viewed as a result of a random walk of particles in which every…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
Levinson's theorem for Dirac particles constraints the sum of the phase shifts at threshold by the total number of bound states of the Dirac equation. Recently, a stronger version of Levinson's theorem has been proven in which the value of…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
This paper proves sharp bounds on the tails of the L\'evy exponent of an operator semistable law on $\mathbb R^d$. These bounds are then applied to explicitly compute the Hausdorff and packing dimensions of the range, graph, and other…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…