Related papers: The finite one-dimensional wire problem
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and…
Conformo static charged dust distributions are investigated in the framework of General Relativity. Einstein's equations reduce to a nonlinear version of Poisson's equations and Maxwell's eqations imply the equaltiy of the charge and mass…
Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires, connected at vertices. In this paper we discuss the solutions of the Schr\"odinger equation on such graphs, which have been named "quantum…
In the spirit of general relativity, spacetime should become curved due to the presence of a particle of a given mass and charge, We try to understand this fact in the quantum theory of a thin shell of matter. It leads to a generalization…
We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
The electrostatic field energy due to two fixed pointlike charges shows some peculiar features concerning the distribution in space of the field energy density of the system. Here we discuss the evaluation of the field energy and the…
This study applies response theory to investigate electron charge dynamics, with a particular focus on charge separation. We analytically assess the strengths and limitations of linear and quadratic response theories in describing charge…
We study the structure of the zero set of a finite point charge electrical field $F = (X,Y,Z)$ in $\mathbb R^3$. Indeed, mostly we focus on a finite point charge electrical field $F =(X,Y)$ in $\mathbb R^2$. The well-known conjecture is…
We study the electric potential and field produced by disordered distributions of charge to see why clumps of charge do not produce large potentials or fields. The question is answered by evaluating the probability distribution of the…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
In this paper, new model for charges distribution is discussed. It is proved that a small charge inside a conductor, no force acts. charge, which is located on the border resistant to small perturbations. The minimum energy of a photon,…
We investigate the equilibrium charge distribution along a single annealed polyelectrolyte chain under different conditions. The coupling between the conformation of the chain and the local charge distribution is described for various…
The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium…
The papers setting upper bounds on the value of electric charge of the photon are briefly reviewed. The theoretical framework of these bounds is shown to be incomplete. Hence the bounds seem to be unreliable.
A generic lattice cut-off model is introduced describing the quantum meandering of a single cuprate stripe. The fixed point dynamics is derived, showing besides free string behavior a variety of partially quantum disordered phases, bearing…
Electromagnetic waves propagate with the speed of light. The reason is that electrostatic fields as well as magnetic fields propagate with this speed. Both types of objects, waves as well as static fields contain and transport energy.…
Recently, some discussions arose as to the definition of charge and the value of the density of charge in stationary-current-carrying conductors. We stress that the problem of charge definition comes from a misunderstanding of the usual…
We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. This electrostatic problem was solved long ago, and its gravitational analogue - even earlier. However, it seems that physics…