Related papers: The universal $\ln^{2}s$ increase in total cross s…
Following Lang and Trotter we describe a probabilistic model that predicts the distribution of primes $p$ with given Frobenius traces at $p$ for two fixed elliptic curves over $\mathbb{Q}$. In addition, we propose explicit Euler product…
We solve the Random Euclidean Matching problem with exponent 2 for the Gaussian distribution defined on the plane. Previous works by Ledoux and Talagrand determined the leading behavior of the average cost up to a multiplicative constant.…
We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the…
In this appendix to our paper with the same title posted on arxiv we give a quick proof of an inequality that can be substituted to Hastings's result, quoted as Lemma 1.9 in our previous paper. Our inequality is less sharp but also appears…
At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the…
We obtain an asymptotic formula for the mean value of L-functions associated to cubic characters over F_q[t]. We solve this problem in the non-Kummer setting when q=2 (mod 3) and in the Kummer case when q=1 (mod 3). The proofs rely on…
We systematically calculate the total reaction cross sections of oxygen isotopes, $^{15-24}$O, on a $^{12}$C target at high energies using the Glauber theory. The oxygen isotopes are described with Slater determinants generated from a…
We study the robustness of self-sustained oscillatory activity in a globally coupled ensemble of excitable and oscillatory units. The critical balance to achieve collective self-sustained oscillations is analytically established. We also…
We consider approaches to the eikonal-like unitarization of elastic amplitude and its generalizations in theories where cross-sections grow with energy, and we discuss corresponding mechanisms of the multiple exchange standing behind it. In…
In this paper, we develop a general homogenization theory for elliptic equations with coefficients that oscillate periodically at infinitely many scales $\varepsilon = (\varepsilon_1, \varepsilon_2, \cdots) \in (0,1)^\infty$, with…
In the theoretical analysis of high-energy elastic nucleon scattering one starts commonly from the description based on the validity of optical theorem, which allows to derive the value of total cross section directly from the…
We show that the accelerated expansion of the Universe can be viewed as a crossover phenomenon where the Newton constant and the Cosmological constant are actually scaling operators, dynamically evolving in the attraction basin of a…
Propagation of a particle accelerated by an external field through a scattering medium is studied within the generalized Lorentz model allowing inelastic collisions. Energy losses at collisions are proportional to $(1-\alpha^{2})$, where…
We have studied the evolution of the Universe in the generalized Einstein action of the form $R+\beta R^2$, where $R$ is the scalar curvature and $\beta=\rm const.$. We have found exact cosmological solutions that predict the present cosmic…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
The variation with energy of the total cross section for elastic electron scattering from atoms of several elements is caused primarily by shape resonances corresponding to the formation of temporary negative ions. It is shown that such…
Fits to high energy data alone cannot cleanly discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of total hadronic cross sections. We demonstrate that this is no longer true when we require that these amplitudes also describe, on…
A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point…
The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential…
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial…