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.

A dissipationless supercurrent state in superconductors can be destroyed by thermal fluctuations. Thermally activated phase slips provide a finite resistance of the sample and are responsible for dark counts in superconducting single photon detectors. The activation barrier for a phase slip is determined by a space-dependent saddle-point (instanton) configuration of the order parameter. In the one-dimensional wire geometry, such a saddle point has been analytically obtained by Langer and Ambegaokar in the vicinity of the critical temperature, $T_c$, and for arbitrary bias currents below the critical current $I_c$. In the two-dimensional geometry of a superconducting strip, which is relevant for photon detection, the situation is much more complicated. Depending on the ratio $I/I_c$, several types of saddle-point configurations have been proposed, with their energies being obtained numerically. We demonstrate that the saddle-point configuration for an infinite superconducting film at $I\to I_c$ is described by the exactly integrable Boussinesq equation solved by Hirota's method. The instanton size is $L_x\sim\xi(1-I/I_c)^{-1/4}$ along the current and $L_y\sim\xi(1-I/I_c)^{-1/2}$ perpendicular to the current, where $\xi$ is the Ginzburg-Landau coherence length. The activation energy for thermal phase slips scales as $\Delta F^\text{2D}\propto (1-I/I_c)^{3/4}$. For sufficiently wide strips of width $w\gg L_y$, a half-instanton is formed near the boundary, with the activation energy being 1/2 of $\Delta F^\text{2D}$.

The sinh-Gordon model is considered on a multi-sheeted Riemann surface with a plane metric and cuts, which connect the sheets. Such a model can be considered as a few copies of the sinh-Gordon model on the plane, connected by special operators (twist operators) that correspond to the end points of the cuts, which are branch points. More complicated operators, composite branch-point twist operators can be considered. They correspond to local operators placed to the branch points. In the present work we calculate form factors of a few series of such operators in the semiclassical limit. The semiclassical approach does not use quantum integrability, but essentially based on exact solutions of the classical model. It allowed us to understand better the renormalization of the local operators.

The pressure-temperature phase diagram of superconducting UTe${}_2$ with three lines of the second- order phase transitions cannot be explained in terms of successive transitions to superconducting states with a decrease in symmetry. The problem is solved using a two-band description of the superconducting state of UTe${}_2$.

It is well known that the anomalous Hall effect in ferromagnetic and strongly paramagnetic metals in addition to electron skew scattering on impurities is determined by internal mechanism linked to the Berry curvature, a quantum-mechanical property of the electron states of a perfect crystal. Experimentally, however, it has been established that the Berry curvature does not play any role in the Hall resistance of the ferromagnet URhGe. URhGe is so called altermagnetic ferromagnet which crystal symmetry includes operation of time inversion only in combination with rotations and reflections. The explanation for strictly zero Berry curvature of electronic states in this material lies in the non-symmorphic symmetry of its crystal lattice.

Processes of interaction of capillary waves were considered both numerically and analytically: merging of two waves into one and wave on the ring (in Fourier space, isotropic spectrum) into larger diameter ring. It was shown numerically, that these processes are the leading ones and other processes with respect to them are at least weaker if manifest themselves at all. In the case of isotropic turbulence of capillary waves the formation of wave turbulence Zakharov-Filonenko spectrum is demonstrated. It was also shown, that in this case one should be cautious about statements of the locality theorem.