相关论文: Steiljes electrostatic model with imaginary charge…
We show that an analog of the physics at the Planck scale can be found in the propagation of tightly focused laser beams. Various equations that occur in generalized quantum mechanics are formally identical to those describing the nonlinear…
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem…
It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. Large class of exact…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
For mathematical models of quantum wave guides we show that in some situations two interacting particles can be trapped more easily than a single particle. In particular, we give an example of a wave guide that can not bind a single…
In this paper, two-dimensional periodic capillary-gravity waves travelling under the effect of a vertical electric field are considered. The full system is a nonlinear, two-layered and free boundary problem. The interface dynamics arises…
We study a boundary value problem related to the search of standing waves for the nonlinear Schr\"odinger equation (NLS) on graphs. Precisely we are interested in characterizing the standing waves of NLS posed on the {\it double-bridge…
In this study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that…
We test the concepts of renormalized charge and potential saturation, introduced within the framework of highly asymmetric Coulomb mixtures, on exactly solvable Coulomb models. The object of study is the average electrostatic potential…
A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling…
It is shown that charged-particle beam transport in the paraxial approximation can be effectively described with a quantum-like picture in semiclassical approximation. In particular, the classical Liouville equation can be suitably replaced…
The focus of the present work is on the Cauchy problem for the quadratic gravity models introduced in \cite{stelle}-\cite{stelle2}. These are renormalizable higher order derivative models of gravity, but at cost of ghostly states…
A model of dense plasmas relying on the superconfiguration approximation is presented. In each superconfiguration the nucleus is totally screened by the electrons in a Wigner-Seitz sphere (ion-sphere model). Superconfigurations of the same…
We present theoretical analysis and numerical studies of the quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized…
We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…
We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational…
A novel two-tiered organization of the microworld is presented, in which only the fundamental quantum fields of the standard model of particle physics (electrons, photons, quarks, etc.) are true quantum waves, exhibiting linear…
We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavior of a spectrum evolving from a broad class of initial data,…