Related papers: The universal $\ln^{2}s$ increase in total cross s…
We derive a universal bound on the integrated total scattering cross-section at \emph{finite} energies, expressed in terms of a single low-energy coefficient constrained by the non-perturbative S-matrix Bootstrap. At high energies, the…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of…
We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to $L^q$ with $q \in [2,\infty)$, we prove a pointwise asymptotic…
We discuss the generalized quantum Lyapunov exponents $L_q$, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which…
We prove the general theorem that the real part of the forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite…
We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's…
A general theory of inhomogeneous broadening is rarely applied to nonlinear spectroscopy in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important third-order nonlinear susceptibility expressions…
We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
Total cross-sections and logarithmic slopes of the elastic scattering cross-sections for different hadronic processes are calculated in the framework of the model of the stochastic vacuum. The relevant parameters of this model, a…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Lyapunov exponents, a purely classical quantity, play an important role in the evolution of quantum chaotic systems in the semiclassical limit. We conjecture the existence of an upper bound on the Lyapunov exponents that contribute to the…
We construct both normal and anomalous deterministic biased diffusions to obtain the Einstein relation for their time-averaged transport coefficients. We find that the difference of the generalized Lyapunov exponent between biased and…
We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system $(X, \mathcal{F}, \mu, T)$ and bounded functions $f_1, f_2 \in L^\infty(\mu)$, there…
The scaling in $\sigma_{\gamma^*p}(W^2, Q^2)$ cross sections (for $Q^2/W^2 << 1$) in terms of the scaling variable $\eta = (Q^2 + m^2_0)/\Lambda^2 (W^2)$ is interpreted in the generalized vector dominance/color-dipole picture (GVD/CDP). The…
The impact of different assumptions about high energy behavior of the total cross section of proton-proton interactions on the ratio of the real to imaginary part of the forward elastic scattering amplitude is analyzed. It is shown how…
Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high…
We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…