Related papers: Flux-Across-Surfaces Theorem for a Dirac Particle
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a…
Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a non-dispersive…
We derive the asymptotic winding law of a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges to an inverse Gamma distribution. For winding…
Quantum-mechanical motion of a half-spin particle was examined in the axially symmetric field of static naked singularities formed by mass distribution with quadrupole moment (q-metric). The analysis was performed by means of the method of…
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…
We first established the dynamic equations to describe the noisy circling motion of a single particle and the corresponding probability conservation equation in both two dimensions and three dimensions, and then developed the evolution…
We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations…
Classical dynamics of spinning zero-size objects in an external gravitational field is derived from the conservation law of the stress-energy and spin tensors. The resulting world line equations differ from those in the existing literature.…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
We prove that strictly convex surfaces moving by $K^{\alpha/2}$ become spherical as they contract to points, provided $\alpha$ lies in the range $[1,2]$. In the process we provide a natural candidate for a curvature pinching quantity for…
The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poschl-Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number…
We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
The flux-across-surfaces conjecture represents a corner stone in quantum scattering theory because it is the key-assumption needed to prove the usual relation between differential cross section and scattering amplitude. We improve a recent…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
It is known that an object translating parallel to a soft wall in a viscous fluid produces hydro- dynamic stresses that deform the wall, which, in turn, results in a lift force on the object. Recent experiments with cylinders sliding under…
We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being…