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We consider a formulation of initial problem for Kolmogorov equation that corresponds a localized source of particles to be scattered by medium with given scattering amplitude density (scattering indicatrix). The multiple scattering…
We study the resonant divergences that occur in quantum scattering cross-sections in the presence of a strong external magnetic field. We demonstrate that all such divergences may be eliminated by introducing radiative corrections to the…
General formulas describing the multiple scattering of electron by polyatomic molecules have been derived within the framework of the model of non-overlapping atomic potentials. These formulas are applied to different carbon molecules, both…
Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the…
We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering…
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges…
We show how the effective equation of motion for a distinguished quantum particle in an ideal gas environment can be obtained by means of the monitoring approach introduced in [EPL 77, 50007 (2007)]. The resulting Lindblad master equation…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the…
For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born…
We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial value conditions. The initial value…
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
We consider electron-atom scattering in a circularly polarized laser field at sufficiently high electron energies, permitting to describe the scattering process by the first order Born approximation. Assuming the radiation field has…
Quantum theory has evolved from a set of provisional rules to an indispensable framework that underlies much of modern technology and infrastructure. Yet, after a century, Born's probability postulate remains at odds with the theory's…