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The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…
The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
We apply the dynamical systems tools to study the asymptotic properties of a cosmological model based on a non-linear modification of General Relativity in which the standard Einstein-Hilbert action is replaced by one of Dirac-Born-Infeld…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
The evolution of static dielectric constants and polarization with doping are analyzed and discussed using established experimental results. The variation of screened Coulomb potential with doping is derived theoretically to justify the…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
Real-time dynamics of charge density and lattice displacements is studied during photoinduced ionic-to-neutral phase transitions by using a one-dimensional extended Peierls-Hubbard model with alternating potentials for the one-dimensional…
Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of…
QCD motivated effective models coupled with the cosmological dilaton field are analyzed. It is shown that all models possess confining solutions with the linear potential of confinement even thought such solutions are not observed in the…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical…
We elaborate on a new representation of Lagrangians of 4D nonlinear electrodynamics including the Born-Infeld theory as a particular case. In this new formulation, in parallel with the standard Maxwell field strength $F_{\alpha\beta},…
The charge dynamical response function of the Hubbard model is investigated on the square lattice in the thermodynamical limit. The obtained charge excitation spectra consist of a continuum, a gapless collective mode with anisotropic…
A new formalism to describe steady-state electronic and thermal transport in the framework of density functional theory is presented. A one-to-one correspondence is proven between the three basic variables of the theory, i.e., the density…
SU(2) Yang-Mills theory coupled in a non-minimal way to two scalar fields is discussed. For the massless scalar fields a family of finite energy solutions generated by an external, static electric charge is found. Additionally, there is a…
A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
In this first of two papers, we develop a steady-state version of classical electrodynamics on the 3-sphere and in hyperbolic 3-space, including an explicit formula for the vector-valued Green's operator, an explicit formula of Biot-Savart…
We derive several new Bogomol'nyi (self-dual) equations in two-species $U(1)\times U(1)$ gauge theories governed by the Born--Infeld nonlinear electrodynamics. By identifying appropriate Born--Infeld type Higgs potentials, we show that the…