Related papers: Borel singularities at small x
Dipole-dipole interaction is a long-range interaction, hence we could expect that the self-consistent field approximation might be applied. In most cases it is correct, but dipolar BECs reveal a surprise. Structure of the self-consistent…
A brief survey is given of recent results on the resummation of leading small-x terms for unpolarized and polarized non--singlet and singlet structure function evolution.
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…
We analyze deep inelastic scattering at small Bjorken x, using the approximate conformal invariance of QCD at high energies. Hard pomeron exchanges are resummed eikonally, restoring unitarity at large values of the phase shift in the dual…
Ultraviolet renormalons, contrary to their infrared counterparts, lead to a universal contribution to the large-order behaviour of perturbative expansions in QCD. In this letter, we determine nature of the leading ultraviolet renormalon…
We study a system of ultra cold dipolar Bose gas atoms confined in a two-dimensional (2D) harmonic trap with a dipolar impurity implanted at the center of the trap. Due to recent experimental progress in dipolar condensates, we focused on…
We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
We study the Borel summability of the small time expansion of the heat kernel associated to a first order perturbation of a Laplacian. An explicit formula for this kernel plays a central role. As a consequence, we get a Poisson formula on…
Bode's sensitivity integral constraints define a fundamental rule about the limitations of feedback and is referred to as the waterbed effect. In a companion paper, we took a fresh look at this problem using a direct approach to derive our…
Using the high energy color dipole formalism, we study the coherent and incoherent nuclear DVCS process in the small-x regime. We consider simple models for the elementary dipole-hadron scattering amplitude that captures main features of…
A model of interacting two dimensional electrons near a Van Hove singularity is studied, using renormalization group techniques. In hole doped systems, the chemical potential is found to be pinned near the singularity, when the…
We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\to iE…
We derive the structure of three-loop anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The contributions of tripole and quadrupole correlations…
In two lectures, we overview the renormalon and renormalon-related techniques and their phenomenological applications. We begin with a single renormalon chain which is a well defined and systematic way to specify the character of…
It is proved that the divergent perturbation expansion for the vacuum polarization by an external constant electric field in the pair production sector is Borel summable in the distributional sense.
In this work we found the new class of exact stationary solutions for 2D-Euler equations. Unlike of already known solutions, the new one contain complex singularities. We consider as complex, point singularities which have the vector field…
The in-plane polarizational stopping power of heavy-ion diclusters in a two-dimensional strongly coupled electron liquid is studied. Analytical expressions for the stopping power of both fast and slow projectiles are derived. To go beyond…
An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…
The status of the resummation of small x contributions to the unpolarized and polarized deep inelastic structure functions is reviewed.