Related papers: A Characteristic Particle Length
The $*$-spread of an ideal is defined as the minimal number of generators of an ideal which is minimal with respect to having the same tight closure as the original ideal. We prove an asymptotic length formula for the $*$-spread.
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation with a potential which is the sum of a periodic function and a general smooth function. We identify two…
It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…
The existence of a characteristic coherence length in FEL SASE Physics determines the independent lasing of different portions, namely the slices, of the electron bunch. Each slice may be characterized by different phase space properties…
People of a race appear different but share a 'phenotypic trait' due to a common genetic origin. Mineral particles are like humans: they appear different despite having a same geological origin. Then, do the particles have some sort of…
It is shown that, in the self-consistent quantum statistical Hartree-Fock approximation, the number of electronic states localized on one nucleus is finite. This result is obtained on the basis of the general electron-nuclear model of…
In a recent paper published in this journal [J. Phys. A: Math. Theor. 42 (2009) 495004] we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power \alpha of their distance…
The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the…
A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter $\alpha$ whose range is determined by the coefficient of friction $\gamma$, that is, $0 \leq \alpha \leq \gamma$. For…
We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the…
Coherent emission of light by free charged particles is ubiquitous in many areas of physics and engineering, with the light's properties believed to be successfully captured by classical electromagnetism in all relevant experimental…
The features of electromagnetic field of relativistic electrons passing through a hole in an absorbing screen as a function of the distance from the screen in range of radiation formation length were investigated. The analysis of obtained…
The Schrodinger equation for a macroscopic number of particles is linear in the wave function, deterministic, and invariant under time reversal. In contrast, the concepts used and calculations done in statistical physics and condensed…
We have studied the optical properties of metallic nanoparticles with arbitrary shape. We performed theoretical calculations of the absorption, extinction and scattering efficiencies, which can be directly compared with experiments, using…
A basic quantity in the characterization of relativistic particles is the proton-to-electron (p/e) energy density ratio. We derive a simple approximate expression suitable to estimate this quantity, U_p/U_e = (m_p/m_e)^(3-q)/2, valid when a…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs. The confidence intervals are adaptive in the sense that they tend to be short…
In this paper we are concerned with nonlinear Schr\"odinger equations with random potentials. Our class includes continuum and discrete potentials. Conditions on the potential $V_{\omega}$ are found for existence of solutions almost sure…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…