Classical Dynamics Of Charged Particle Research Articles

On the classical dynamics of charged particle in special class of spatially non-uniform magnetic field

Motion of a charged particle in uniform magnetic field has been studied in detail, classically as well as quantum mechanically. However, classical dynamics of a charged particle in non-uniform magnetic field is solvable only for some specific cases. We present in this paper, a general integral equation for some specific class of non-uniform magnetic field and its solutions for some of them. We also examine the supersymmetry of Hamiltonians in exponentially decaying magnetic field with radial dependence and conclude that this kind of non-uniformity breaks supersymmetry.

Diffusion in Deterministic Interacting Lattice Systems.

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by MonteCarlo simulations.

Affine connection structure of the charged symplectic 2-form

It is shown that the charged symplectic form in Hamiltonian dynamics of classical charged particles in electromagnetic fields defines a generalized affine connection on an affine frame bundle associated with spacetime. Conversely, a generalized affine connection can be used to construct a symplectic 2-form if the associated linear connection is torsion-free and the antisymmetric part of theR 4* translational connection is locally derivable from a potential. Hamiltonian dynamics for classical charged particles in combined gravitational and electromagnetic fields can therefore be reformulated as aP(4)=O(1, 3)⊗R 4* geometric theory with phase space the affine cotangent bundleAT * M of spacetime. The sourcefree Maxwell equations are reformulated as a pair of geometrical conditions on the ℝ4* curvature that are exactly analogous to the source-free Einstein equations.