Related papers: A rigorous lower bound on the scattering amplitude…
Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit,…
In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy $s$-wave correlated pair and spectator particles, while terms that include energy…
We generalize the Froissart-Martin upper bound for the scattering amplitude in spaces with compactified extra dimensions.
This manuscript, presented to receive habilitated doctor degree, contains an overview of my recent works in developing complex scaling method and its applications in the few-body physics.
The problem of describing low-energy two-body scattering for systems with two open channels with different thresholds is addressed in the context of an effective field theory. In particular, the problem where the threshold is unnaturally…
We give a partly new proof of the fluctuation bounds for the second class particle and current in the stationary asymmetric simple exclusion process. One novelty is a coupling that preserves the ordering of second class particles in two…
A method of calculation of the scattering amplitude for fermions and scalar bosons with exchanging of a scalar particle in ladder approximation is suggested. The Bethe-Salpeter ladder integral equations system for the imaginary part of the…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the…
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
The validity range of the widely used traditional effective range expansion can be severely limited by the presence of a left-hand cut near the two-particle threshold. Such a left-hand cut emerges in two-particle scattering processes…
We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…
Light scattering is one of the most established wave phenomena in optics, lying at the heart of light-matter interactions and of crucial importance for nanophotonic applications. Passivity, causality and energy conservation imply strict…
We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed…
We present a practical method to obtain bounds for the oscillation minima and maxima of large classes of biochemical oscillator models that generate oscillations through a negative feedback. These bounds depend on the feedback nonlinearity…
The generalization of the conformal scattering method for small-angle scattering processes involving magnetic monopoles and ordinary charges is constructed. Using this generalization we show that introducing of magnetic charges corresponds…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…
On-shell scattering amplitudes have proven to be useful tools for tackling the two-body problem in general relativity. This thesis outlines how to compute relevant classical observables that are themselves on-shell, directly from…
In the context of non-relativistic quantum mechanics, we obtain several upper and lower limits on the mean square radius applicable to systems composed by two-body bound by a central potential. A lower limit on the mean square radius is…