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The Novikov problem on the level lines of quasiperiodic potentials on a plane with additional (quasi-crystalline) symmetry is considered. For potentials of this type, the possibility of the emergence of open level lines at only a single energy level is shown in the general case. Possible estimates of the growth rate of closed level lines as the energy approaches the percolation threshold are also discussed.

We study triggered by an a.c. external electric field weakly nonlinear stages of flexoelectric instability in nematic liquid crystals. The instability occurs at a finite wave vector. We analyze behavior on time scales much larger than the period of the external electric field. We focus on the case where the increment of the most-unstable mode has an imaginary part, so-called Hopf bifurcation. The existence of such regime was established in our previous work [E.S. Pikina, A.R. Muratov, E.I.Kats, V.V. Lebedev, Dynamic flexoelectric instabilities in nematic liquid crystals, Phys. Rev. E, 110, 024701 (2024)]. Then above the instability threshold a variety patterns of nematic director distortions could appear including standing and travelling structures. Our numerical simulations based on the full nonlinear electro-nematodynamics system of equations. We found that the stable dynamic pattern in the vicinity of the Hopf bifurcation travelling oblique rolls of the nematic director distortions. The establishment of this regime occurs abnormally slowly, which is determined not only by the critical Landau-like slowdown of dynamics, but also by the presence of a long-lived intermediate unstable but long-lived dynamic patterns oscillating in time (standing but not traveleling rolls). Depending on liquid crystal material parameters, the bifurcation corresponding to the formation of the travelling oblique rolls, can be soft (i.e.continues, ‘’critical’’ or close to ‘’tricritical’’ one), or hard (discontinues).

Мы развиваем феноменологическую теорию, описывающую взаимодействие сверхпроводящего конденсата с Бесселевым пучком структурированного (закрученного) света, характеризуемого ненулевым орбитальным угловым моментом $m$. Стартуя с нестационарной теории Гинзбурга-Ландау с комплексной константой релаксации, мы вычисляем пространственные распределения стационарных (dc) фотоиндуцированных токов и магнитных полей, а также отклик на второй гармонике. Мы показали, что фототоки и магнитные поля определяются как поляризацией света, так и его орбитальным моментом $m$. Мы проанализировали две различные геометрии: сверхпроводящего полупространства и тонкой плёнки. В конце мы обсуждаем возможные экспериментальные методики для измерения сверхпроводящих фототоков и соответствующих магнитных полей.

The unitarity of the 4D lattice theory of gravity in the case of the Minkowski signature is proved. The proof is valid only for lattices that conserve the number of degrees of freedom during time evolution. The Euclidean signature and the Minkowski signature are related by the deformation of the integration contours of dynamic variables in a discrete lattice functional integral. It is important that the result is obtained directly on the lattice. Since the studied lattice theory of gravity in the long-wave limit transforms into the well-known Einstein-Cartan-Palatini theory, the obtained result means that this lattice theory of gravity has the right to be considered as a discrete regularization of the generally accepted continuous physical theory of gravity.

Layered van der Waals crystals of topologically non-trivial and trivial semimetals with antiferromagnetic (AFM) ordering of magnetic sublattice are known to exhibit a negative magnetoresistance that is well correlated with AFM magnetization changes in a magnetic field. This effect is reported in several experimental studies with EuFe2As2, EuSn2As2, EuSn2P2, etc., where the resistance decreases quadratically with field by about 5% up to the spin-polarization field. Although this effect is well documented experimentally, its theoretical explanation is missing up to date. Here, we propose [1] a theoretical mechanism describing the observed magnetoresistance that is inherent in AFM metals and is based on violation the binary symmetry. It is almost isotropic to the field and current directions, contrary to the known mechanisms such as giant magnetoresistance and chiral anomaly. The proposed intrinsic mechanism of magnetoresistance is strong in a wide class of the layered AFM-ordered semimetals. The theoretically calculated magnetoresistance is qualitatively consistent with experimental data for crystals of various composition. [1]. Pavel D. Grigoriev, Nikita S. Pavlov, Igor A. Nekrasov, Igor R. Shein, Andrey V. Sadakov, Oleg A. Sobolevskiy, Evgeny Maltsev & Vladimir M. Pudalov, Universal negative magnetoresistance in antiferromagnetic metals from symmetry breaking of electron wave functions, Communications Materials 6, 252 (2025) (Springer Nature)

We study [1] the effects of imperfect nesting in the density wave (DW) state on various electronic properties within a simple two-dimensional tight-binding model. The discussed model reflects the main features of quasi-1D metals where the DW emerges. We show that a DW with imperfect nesting leads to unusual singularities in the quasiparticle density of states and to a power-law renormalization of the superconducting critical temperature. Our results are derived at arbitrary large antinesting and may help to understand the phase diagram of the wide class of density wave superconductors. We also compute the conductivity tensor in a wide temperature range, including the DW transition, and obtain a satisfactory agreement with the experimental data on rare-earth trichalcogenides and many other DW materials. [1] A.V. Tsvetkova, Ya.I. Rodionov, P.D. Grigoriev, Resistivity, density of electronic states, and superconducting transition temperature in density wave compounds with imperfect nesting, Phys. Rev. B 111, 205141 (2025).

It has been shown that negative ions that do not exist in a vacuum or under normal conditions can be created and studied in liquid helium. These negative ions often have a triplet ground state, which we studied for ions of the first-row chemical elements in the periodic table: hydrogen, lithium, sodium, potassium, and cesium. Theoretical estimates of their energy and other parameters in liquid helium have been obtained.

Classical works, dedicated to the finite-gap intrgration, admits the following interpretation. One has g finite circles on the spectral curve, and each oval contains exactly one zero of the wave function. A set of g circles is exactly the g-dimensional torus, which is exactly the Liouville torus. The Abel transform linearizes the motion of this tours. If one consideres degenerate curves, corresponding to the multisoliton solutions, the defintion of divisors requires a refinement, including the resolution of singularities. We show that for the so-called MM-curves and Dubrovin-Natanzon divisors, generating real regular multisoliton KP-2 solutions, it is sufficient to apply only the two simplest types of resolutions.

Recently, a big number of papers dedicated to the study of PT-symmetric operators and integrable equations has been published. In the finite-gaps approach to the 1-d Schrodinger operators two alternative approaches can be used: 1) Matvees-Its approach based on the theory of Riemann theta-functions; 2) Dubrovin's approach based on the divisor's dynamics. The characterization of PT-symmetric Schrodinger operators in the first approach was recentky obtained by Taimanov. In our parer we describe the spectral curves and divisor trajectories for such operators in the first-order approximation.