相关论文: Flux-Across-Surfaces Theorem for a Dirac Particle
We discuss the property of the number density of a fluid of particles living in a curved surface without boundaries to be constant in the thermodynamic limit. In particular we find a sufficient condition for the density to be constant along…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
Diffusion of a tagged particle near a constraining biological surface is examined numerically by modeling the surface-water interaction by an effective potential. The effective potential is assumed to be given by an asymmetric double well…
The probability of a quantum particle being detected in a given solid angle is determined by the $S$-matrix. The explanation of this fact in time dependent scattering theory is often linked to the quantum flux, since the quantum flux…
In the realm of relativistic quantum mechanics, we address a fundamental question: Which one, between the Dirac or the Foldy-Wouthuysen density, accurately provide a probability density for finding a massive particle with spin $1/2$ at a…
Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the…
The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2,…
The classical fluid dynamics boundary condition of no-slip suggests that variation in the wettability of a solid should not affect the flow of an adjacent liquid. However experiments and molecular dynamics simulations indicate that this is…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
We consider the area-preserving Willmore evolution of surfaces that are close to a half-sphere with a small radius, sliding on the boundary S of a domain while meeting it orthogonally. We prove that the flow exists for all times and keeps a…
The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a…
Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the…
In this introductory review article, we explore the special relativistic equations of particle motions and the consequent derivation of Einstein's famous formula $E=mc^2$. Next, we study the special relativistic electromagnetic field…
In 1905, Einstein's theory of Brownian motion supported the molecular basis of the diffusion equation and introduced two complementary viewpoints: a deterministic field description and a probabilistic formulation based on stochastic…
The phenomenon of spin-dependent quantum scattering in two-dimensional (2D) pseudospin-1/2 Dirac materials leading to a relativistic quantum chimera was recently uncovered. We investigate spin-dependent Dirac electron optics in 2D…
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to…