相关论文: The geometrical nature and some properties of the …
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
The properties of quintessence are examined through the study of the variation of the electromagnetic coupling. We consider two simple quintessence models with a modified exponential potential and study the parameter space constraints…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
We discuss an investigation exploring students' difficulties with equations involving resistance, capacitance and inductance. We find that introductory physics students have great difficulty understanding, e.g., how the resistance of an…
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…
Casimir interactions between macroscopic objects are strongly influenced by their geometrical features as shape and orientation as well as by their material properties. The effect of geometry is commonly obtained from the proximity…
We derive the electric and magnetic form factors of the neutron in the framework of a relativistic constituent quark model. Our parameter free prediction agrees well with a recent, accurate measurement. The relativistic features of the…
The variance of observables of quantum states of the Laplacian on the modular surface is calculated in the semiclassical limit. It is shown that this hermitian form is diagonalized by the irreducible representations of the modular quotient…
We give a criterion for H-convergence of conductivity matrices in terms of ordinary weak convergence of the factors in certain quotient representations of the matrices.
A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the…
Electromagnetic properties of quark-like particles are examined in a classical field model involving extended dual electromagnetic fields. These can have fractional charges and a confining potential that derives essentially completely from…
We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis…
Relations have been derived which establish connection between a scalar or a vector functions and the integral of Laplace operator of these functions (the integral property of Laplace operator). The integral property of Laplace operator was…
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple…
The conductance in an extended multiband Hubbard model describing linear arrays of up to ten quantum dots is calculated via a Lanczos technique. A pronounced suppression of certain resonant conductance peaks in an applied magnetic field due…
Formulas for the contribution of the conduction electrons to the polarization and magnetization are derived for disordered systems and within a one-particle framework. These results generalize known formulas for Bloch electrons and the…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conjugate of a real matrix attract, we derive expressions for…
Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this…