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.

In 3D turbulent flows of a rotating system, where the Coriolis force prevails over the inertia in dynamics, formation of the columnar vortices takes place that is observed both experimentally [1] and numerically [2]. They are large-scale coherent flows that are homogeneous along the axis of rotation. Our work is about to build analytical model describing how axisymmetric vortex flow supports itself by absorbing inertial waves. We consider the following pumping mode: inertial waves reach the vortex from the periphery of system, where turbulence is excited. In the limits of short wavelengths and low viscosity we show that quasi-monochromatic wave that enters in the vortex transmits its energy and momentum only in the narrow vicinity of its critical layer [3] formed by an average shear flow. In our model we determine the Reynolds shear stress component averaged over inertial wave ensemble that sets the velocity profile of vortex [4].

[1] D.D. Tumachev, A.A. Levchenko, S.S. Vergeles, S.V. Filatov, Observation of a large stable anticyclone in rotating turbulence, PoF, 36(12), 126620 (2024).
[2] Seshasayanan, K. & Alexakis, A. Condensates in rotating turbulent flows. JFM, 841, 434–462 (2018).
[3] Haynes, P., 2015. Critical Layers. In: G. R. North et al., Encyclopedia of Atmospheric Sciences, 2nd edition, Vol 2.
[4] I.V. Kolokolov, L.L. Ogorodnikov, and S.S. Vergeles, Structure of coherent columnar vortices in three-dimensional rotating turbulent flow, Phys. Rev. Fluids 5, 034604 (2020).

We investigate analytically and numerically the statistical properties of the dynamics of rigid spherical particles with neutral buoyancy. The particles are placed in a turbulent flow with a strong shear component. As a simple model, we consider the shear flow of an axisymmetric vortex with turbulent fluctuations and calculate the particle distribution from the distance to the vortex center. We present quantitative results obtained within the framework of a point particle model with fluctuations that are correlated in time.