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Depolarization of quantum fields is handled through a master equation of the Lindblad type. The specific feature of the proposed model is that it couples dispersively the field modes to a randomly distributed atomic reservoir, much in the…
A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is…
We show that the Einstein covariance principle provides an opportunity to generate infinitely many solutions of given covariant equation from a known one. With use of this statement we derive exact expressions for charge and current…
We use blow-up solutions of nonlinear Helmholtz equations to introduce a nonlinear resonance effect that is capable of amplifying electromagnetic waves of particular intensity. To achieve this, we propose a scattering setup consisting of a…
Image inpainting involves filling in damaged or missing regions of an image by utilizing information from the surrounding areas. In this paper, we investigate a highly nonlinear partial differential equation inspired by the modified…
This paper is concerned with the energy decay and the finite time blow-up of the solution to a viscoelastic wave equation with polynomial nonlinearity and weak damping. We establish explicit and general decay results for the solutions by…
Photoionization of an atom in the presence of a neighboring atom of different species is studied. The latter first undergoes resonant photoexcitation, leading to an autoionizing state of the diatomic system. Afterwards, the excitation…
The photon bremsstrahlung rate from a quark jet produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. The leading medium-enhanced higher twist corrections which describe the multiple scattering…
Newly observed enhanced linear optical features of fullerene solutions (Raman scattering and one-photon luminescence) are due to clusterization of fullerene molecules themselves as well as their composites with solvent molecules. A direct…
With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is,…
A non-isotropic version of phase equations such as the Burgers equation, the K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney equation in the three-dimensional space is systematically derived from a general…
A peculiar radiation arising as a result of radiation interference of nonlinear oscillators excited by a monochromatic plane wave field of the incident particle is described. The radiation properties are determined by the fact that a phase…
I classify multiphoton absorption into separable, linked, and simultaneous processes. The first and second types can be distinguished when the rate-equation approximation is valid whereas the third type refers to the case when the full…
We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension (1D) for both positive and negative signs of the nonlinear term, as…
Scattering of resonant radiation in a dense two-level medium is studied theoretically with account for local field effects and renormalization of the resonance frequency. Intrinsic optical bistability is viewed as switching between…
The aim of this paper is to obtain estimates for the density of the law of a specific nonlinear diffusion process at any positive bounded time. This process is issued from kinetic theory and is called Landau process, by analogy with the…
A wave front propagating through a medium is described using the Ising--Bloch method The reaction-diffusion behaviour of an autocatalysis model of incoming waves from energetic material in a nitroguanidine lens and its interactions with…
The illumination of an accretion disk around a black hole or neutron star by the central compact object or the disk itself often determines its spectrum, stability, and dynamics. The transport of radiation within the disk is in general a…
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does…
Among the emerging technologies with prophesied quantum advantage, quantum communications has already led to fascinating demonstrations -- including quantum teleportation to and from satellites. However, all optical communication…