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.

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.

We perform calculations of the nuclear modification factors $R_{AA}$ and $I_{AA}$ for collisions of light nuclei at the LHC energies for scenarios with and without quark-gluon plasma formation in pp collisions. We find a sizeable difference in $R_{AA}$ and $I_{AA}$ for these two scenarios, which grows with decreasing atomic number. This says that data on the nuclear modification factors for light nuclei could give information on the presence of jet quenching in pp collisions. Preliminary data from the CMS Collaboration on O+O and Ne+Ne collisions obtained in 2025 support the scenario with quark-gluon plasma formation in pp collisions.

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.

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).

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)

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.

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.

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).

This year, our colleague and teacher Vladimir Mineev turns 80. During the workshop on December 5, 2025, we will celebrate his contributions to theoretical condensed-matter physics. His friends, students, and colleagues will share their research results and recent advancements in this field.

The workshop will be held in a hybrid format, with both on-site and online participation.

Please visit mineev80.itp.ac.ru for details

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 develop a theoretical framework, using the slow variables method in the RSJ model, and perform numerical simulations to explain the peculiarities of the Josephson diode effect observed in an asymmetric SQUID with a superconducting nanobridge and an SNS junction in recent experiments by Vasiliy Stolyarov’s group at MIPT. For this case we predict the new (amplitude) mechanism of the diode effect which originates from the presence of a superconducting nanobridge exhibiting a multivalued current-phase relation (CPR). Theoretically, this mechanism manifests itself in the dependence of the amplitude of the first Josephson harmonic in the CPR of the SQUID on the current direction. We demonstrate that this mechanism accounts for the experimentally observed pronounced asymmetry of the Shapiro steps, which coexists with a relatively small asymmetry in the critical current. Additionally, we investigate how the diode efficiency (quantified via the Shapiro steps asymmetry) depends on both the magnetic flux through the superconducting loop and the power of the external microwave irradiation. Our theoretical predictions are found to be in good agreement with the experimental observations. This talk is based on the article Phys. Rev. B 112, 144504 (2025).

Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resistively Shunted Junction (RSJ) model, an important example of a nonlinear dynamical system. The standard RSJ model considers an overdamped JJ with a sinusoidal (single-harmonic) current-phase relation (CPR) in the current-driven regime with a monochromatic ac component. While this model predicts only integer Shapiro steps, the inclusion of higher Josephson harmonics is known to generate fractional Shapiro steps. In this paper, we show that only two Josephson harmonics in the CPR are sufficient to produce all possible fractional Shapiro steps within the RSJ framework. Using perturbative methods, we analyze amplitudes of these fractional steps. Furthermore, by introducing a phase shift between the two Josephson harmonics, we reveal an asymmetry between positive and negative fractional steps — a signature of the Josephson diode effect.

This talk presents results of a comprehensive study of the classical and quantum dynamics of spin 1/2 Dirac fermion particles with dipole moments under the action of arbitrary external fields (including gravitational, inertial, electromagnetic, axion ones). The gauge-theoretic framework of the general-relativistically covariant Dirac theory is used to describe in a consistent way the minimal and nonminimal couplings of fermions to external fields of different physical nature. The quantum and quasiclassical equations of motion are derived and a complete consistency of the quantum and classical spin dynamics is demonstrated. Applications range from astrophysics, to precision experiments with polarized particles in accelerators and storage rings, to the heavy-ion collisions.

I will make a few comments on heavy tetraquarks using the gauge/string duality. In particular, I describe the structure of the two low-lying Born-Oppenheimer potentials.