We consider the Novikov problem of describing the geometry of level lines of quasi-periodic functions on the plane. We describe here the most general case, when the number of quasi-periods of a function is not limited. The main subject of investigation is the emergence of open level lines or closed level lines of arbitrarily large sizes, which play an important role in many dynamical systems related to the general Novikov problem. As can be shown also, the results obtained for quasiperiodic functions on the plane can be generalized to the multidimensional case. In this case, we are dealing with a generalized Novikov problem, namely, the problem of describing level surfaces of quasiperiodic functions in a space of arbitrary dimension.

We consider a special behavior of the magnetic conductivity of metals that arises when chaotic electron trajectories appear on the Fermi surface. This behavior is due to the scattering of electrons at singular points of the dynamic system describing the electron motion in the quasimomenta space, and caused by small-angle scattering of electrons on phonons. In this situation, the electronic system is described by a ``non-standard'' relaxation time, which plays the main role in a certain range of temperature and magnetic field values.

We examine a general class of models involving a two-band fermion system subjected to dissipation, conserving the total number of particles. By construction, these models have a guaranteed steady state – a dark state – with a completely filled lower band and an empty upper band. In the limit of weak dissipation, we derive equations governing the dynamics of the fermion densities over long length and time scales. These equations belong to the Fisher-Kolmogorov-Petrovsky-Piskunov reaction-diffusion universality class. Our analysis reveals that the engineered dark state is generically unstable, giving way to a new steady state with a finite density of particles in the upper band. Our results suggest that number-conserving dissipative protocols may not be a reliable universal tool for stabilizing dark states.
arXiv:2408.04987

The ALT - Advanced Laser Technologies conference was held on 23-27 September 2024. The conference website https://altconference24.ru/ The FEFU (Far Eastern Federal University) buildings on Russky Island were used for presentations. A wide range of issues on laser technologies from quantum computing and biophotonics to plasmonics, sensors, THz and fibre optics were considered. As a result, an appeal to the President of the Russian Academy of Sciences G.Ya. Krasnikov was adopted. The appeal emphasises the importance of the directions related to photonics.

When considering quantum processes rendered by copious absorptions of soft photons like the non-linear Compton scattering, it is common to postulate the strong-field interaction regime. However, upon closer examination this `strong-field regime' falls into several sub-regimes. They are conditional on invariant parameters such as the non-linearity parameter $a_0$ proportional to the field amplitude, and the dynamical quantum parameter $\chi$, which denotes the field amplitude experienced by a particle in its reference frame in the units of the critical (Schwinger) field of QED $E_S=m^2c^3/e\hbar$ (here, $m$ and $-e$ are the electron mass and charge) [1].
An electron injected into a strong field with high $a_0 >> 1$ rapidly become ultra-relativistic and can emit strong radiation, and at $\chi > 1$ the emission process is essentially quantum. In this regime, radiation dominates particle dynamics, and production of new electron-positron pairs by hard photons in a strong field becomes important. This can reveal, for example, in QED cascades [1], which in some cases can be sustained by the field leading to abundant production of pairs [2,3].
The Furry picture, which is at the core of the strong-field QED approach, allows building the perturbative scattering theory in a strong external electromagnetic field that is accounted for exactly. Under the so-called locally constant field approximation (LCFA) for processes involving relativistic particles in transverse fields, the model of a uniform constant crossed field (CCF) appears to be universal, and at the same time allows analytical treatment for many processes.
At very high $\chi >> 1$, the loop contributions to scattering amplitudes (so-called polarisation and mass operators) in a CCF grow surprisingly fast, namely, as a power of the field strength and particle energy entering the parameter $g = \alpha\chi^{2/3}$. As was initially conjectured by Narozhny [4], and later confirmed by our all-order calculation [5], $g^n$ factors the leading-type n-th loop contributions in the perturbation expansion, meaning that at $g>1$ the Furry expansion breaks down and renders the new fully non-perturbative regime of strong-field QED. Strikingly, this regime arises at scales that could be feasible in future experiments.
In this talk, we review the above mentioned regimes of strong-field QED, the related theoretical framework, and the connection to possible future experiments.
[1] A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Phys. Rep. 1010, 1 (2023).
[2] A. R. Bell and J. G. Kirk, PRL 101, 200403 (2008).
[3] A. Mercuri-Baron, A.A, Mironov, C. Riconda, A. Grassi, M. Grech, arXiv:2402.04225 (2024).
[4] N. B. Narozhny, Expansion parameter of perturbation theory in intense-field quantum electrodynamics, Physical Review D 21, 1176 (1980).
[5] A. A. Mironov, S. Meuren, and A. M. Fedotov, PRD 102, 053005 (2020); A. A. Mironov and A. M. Fedotov, PRD 105, 033005 (2022).

We investigate here the deformations of Berglund Hübsch loop and chain mirrors where the original manifolds are defined in the same weighted projective space. We show that the deformations are equivalent by two methods. First, we map directly the two models to each other and show that the deformations bare the same for 79 ”Good” models, but not for the 77 ”Bad” ones. We then investigate the orbifold of the mirror pair by the maximal symmetry group and show that the number of deformations is the same and that they are almost thesame, i.e., the first four exponents of the deformations are identical.
https://doi.org/10.1016/j.Nucl-PhysB.2024.116695
http://arxiv.org/abs/2408.15182