Related papers: Path distributions for describing eigenstates of o…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…
Levy walk at the finite velocity is considered. To analyze the spatial and temporal characteristics of this process, the method of moments has been used. The asymptotic distributions of the moments (at $t\to\infty$) have been obtained for…
In this paper we develop a general formalism of a path approach for non-equilibrium statistical mechanics. Firstly, we consider the classical Gibbs approach for states and find that this formalism is ineffective for non-equilibrium…
This paper is devoted to study the propagation of light beams carrying orbital angular momentum in optically anisotropic media. We first review some properties of homogeneous anisotropic media, and describe how the paraxial formalism is…
In this letter we consider the phase diffusion of a harmonically driven undamped pendulum and show that it is anomalous in the strong sense. The role played by the fractal properties of the phase space is highlighted, providing an…
The diffusions and anomalous diffusions of charged particles in the plateau regime of toroidal plasma with a Maxwellian velocity distribution are studied. The transport theory of plasma is discussed under the toroidal coordinate system and…
Predicting human behavior is a difficult and crucial task required for motion planning. It is challenging in large part due to the highly uncertain and multi-modal set of possible outcomes in real-world domains such as autonomous driving.…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space. These functions can be obtained through a Fourier transform in the transverse space of the generalized…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
We introduce a new class of nondiffracting optical pulses possessing orbital angular momentum. By generalizing the X-waves solution of the Maxwell equation, we discover the coupling between angular momentum and the temporal degrees of…
Planets form in active protoplanetary disks that sustain stellar jets. Momentum loss from the jet system may excite the planets' orbital eccentricity and inclination (Namouni 2005, AJ 130, 280). Evaluating quantitatively the effects of such…
In this paper we investigate the transport of energetic particles in turbulent plasmas. A numerical approach is used to simulate the effect of the background plasma on the motion of energetic protons. The background plasma is in a…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
Illumination of a two-dimensional system by a twisted light beam is considered in order to find specific effects caused by twisting. Direct interband transitions between the valence and conduction bands are supposed. The generation rates of…
We calculate the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal in- teraction. For that we apply the statistical method of Chandrasekhar (1943),…
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…