Quantum regime of laser-matter interactions at extreme intensities

A survey of physical parameters and of a ladder of various regimes of laser-matter interactions at extreme intensities is given. Special emphases is made on three selected topics: (i) qualitative derivation of the scalings for probability rates of the basic processes; (ii) self-sustained cascades (which may dominate at the intensity levels attainable with next generation laser facilities); and (iii) possibility of breaking down the Intense Field QED approach for ultrarelativistic electrons and high-energy photons at certain intensity level.Comment: To be published in the Proceedings of the Summer School "Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks" (18-30 July 2016, BLTP, JINR, Dubna, Russia

An exact renormalization formula for Gaussian exponential sums and applications

In the present paper, we derive a renormalization formula "\`a la Hardy-Littlewood" for the Gaussian exponential sums with an exact formula for the remainder term. We use this formula to describe the typical growth of the Gaussian exponential sums

Geometric tools of the adiabatic complex WKB method

The paper is devoted to the description of the main geometric and analytic tools of a complex WKB method for adiabatic problem. We illustrate their use by numerous examples

Probabilistic approach to a proliferation and migration dichotomy in the tumor cell invasion

The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. The transport of tumor cells is formulated in terms of the CTRW with an arbitrary waiting time distribution law, while proliferation is modelled by a logistic growth. The overall rate of tumor cell invasion for normal diffusion and subdiffusion is determined.Comment: Accepted for publication as a Regular Article in Physical Review

On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line

In this paper, we study spectral properties of a family of quasi-periodic Schrodinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curves are extended along the momentum direction. In the energy intervals where this happens, we obtain an asymptotic formula for the Lyapunov exponent, and show that the spectrum is purely singular