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Within the non-relativistic potential scattering theory, we derive a generalized version of the L\"uscher formula, which includes three-particle inelastic channels. Faddeev equations in a finite volume are discussed in detail. It is proved…
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…
Making use of the analytical properties of the $S$-matrix and a theorem of Mittag-Leffler, model independent non-relativistic expressions for cross sections in single channel elastic scattering, scattering phase shifts and survival…
This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…
Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov…
From the perspective of the theory of operator semigroups, we reflect back on the classical theorem of Portenko devoted to approximation of skew Brownian motion. The theorem says that by concentrating the power of drift of a diffusion…
A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as…
We derive closed analytical formulae for the power emitted by moving charged particles in a uniaxial wire medium by means of an eigenfunction expansion. Our analytical expressions demonstrate that in the absence of material dispersion the…
A unified equation is employed to analytically investigate the scattering of massless spin particles by a Schwarzschild-type medium black hole. It is found that for spin particles, curved spacetime induces an effective complex potential…
We present a computer program which solves the Schrodinger equation of the stationary states for an average nuclear potential of Woods-Saxon type. In this work, we take specifically into account triaxial (i.e. ellipsoidal) nuclear surfaces.…
We present compact analytic expressions for 3-flavor neutrino oscillation probabilities with invisible neutrino decay, where matter effects have been explicitly included. We take into account the possibility that the oscillation and decay…
We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…
Structures in the invariant mass distribution are often linked to unstable intermediate states or resonances. In experiments, many signals are detected which have broad, overlapping or intricate profiles, which makes their characterization…
During comprehensive study of weakly nonlinear interaction of surface capillary waves, processes of resonant and non-resonant interactions were considered both numerically and analytically: merging of two waves into one and waves on the…
A production representation of partial-wave $S$ matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated…
We consider the one-dimensional Schr\"odinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line $x\ge 0$. For this equation at fixed positive energy we give…
The longest-range part of the nuclear force due to the one-pion exchange governs the energy dependence of the scattering amplitude in the near-threshold region and imposes correlations between the coefficients in the effective range…
The aim of the article to clarify the status of Shapiro plane wave solutions of the Schr\"odinger's equation in the frames of the well-known general method of separation of variables. To solve this task, we use the well-known cylindrical…
Flux-integrated semiexclusive differential cross sections for charged-current quasielastic and neutral-current elastic neutrino scattering on argon are analyzed. The cross sections are calculated using the relativistic distorted-wave…
We have calculated the one-loop scattering amplitude of an electron by an external Coulomb potential in QED free of infrared divergences. This feature is achieved by applying the Faddeev-Kulish formalism, which implies a redefinition of…