Related papers: Features of Moyal Trajectories
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be…
A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is…
H\"older functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Special subsets of orbits in chaotic systems, e.g. periodic orbits, heteroclinic orbits, closed orbits, can be considered as skeletons or scaffolds upon which the full dynamics of the system is built. In particular, as demonstrated in…
Moyal-deformed hierarchies of soliton equations can be extended to larger hierarchies by including additional evolution equations with respect to the deformation parameters. A general framework is presented in which the extension is…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
Besides its various applications in string and D-brane physics, the $\theta$-deformation of space (-time) coordinates (naively called the noncommutativity of coordinates), based on the $\star$-product, behaves as a more general framework…
Meridional circulation in stratified stellar/planetary interiors in the presence of stable molecular weight gradients remains poorly understood, thereby affecting angular momentum transport in evolutionary models. We extend the downward…
Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…
In this section, we examine the transition from statistically homogeneous turbulence to inhomogeneous turbulence with zonal flows. Statistical equations of motion can be derived from the quasilinear approximation to the Hasegawa-Mima…
We study the eikonal approximation to quantum mechanics on the Moyal plane. Instead of using a star product, the analysis is carried out in terms of operator-valued wavefunctions depending on noncommuting, operator-valued coordinates.
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with…
We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients.…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…