We present an idea of a new method to measure spin-orbit scattering rate in strongly disordered superconducting materials. The method is based upon specific Andreev reflection phenomenon at the boundary between superconductor and half-metal (fully polarized metallic ferromagnet). We demonstrate theoretically that spin-orbit scattering leads to a formation of a fluctuating in space triplet component of superconducting order parameter ∆_p(r) with zero average. However, Andreev conduction to half-metal is allowed due to mesoscopic fluctuations of this order parameter. The effect is expected to be strong in superconducting materials like amorphous InOx and others with not very large values of kF l product.

An energy level E in a quantum or wave scattering problem is called a transmission eigenvalue if one can prepare the incoming wave in such a way that no scattered wave is present. The dimension of the kernel of the scattering operator is called the transmission eigenvalue multiplicity. A typical results in this area states that for regular potentials with compact support the transmission eigenvalues 1) have finite multiplicity and 2) form a discrete set. We explain that such results have limited applicability because 1) In 1995 we proved that in dimension 2 one can construct regular decaying faster than any degree of the distance from the origin potentials, transparent at one energy. 2) Mutlipoint scatterers have transmission eigenvalues of infinite multiplicity at all energies.

Magneto-electric effect, that is an appearance of magnetisation induced by electric current is allowed by symmetry in metals with crystal structure without space inversion. The microscopic origin of this effect is spin-orbit coupling of electrons with a non-centrosymmetric crystal lattice lifting spin degeneracy of electron energy and mixing spin and orbital degrees of freedom. The presented calculation of magnetisation induced by current based on the application of kinetic equation for the matrix distribution function of electrons occupying the states in two bands split by the spin-orbit interaction.
arXiv:2312.04592

A theory of strong coupling superconductivity in uranium compounds has been developed, based on electron-electron interaction through magnetic fluctuations described by frequency-dependent magnetic susceptibility. The magnetic field dependence of the electron effective mass is expressed through the field dependence of the magnetic susceptibility components. It is shown that the intensity of triplet pairing, and hence the critical temperature of the transition to the superconducting state, is also determined by the field-dependent susceptibility. The results are discussed in relation to the properties of ferromagnetic uranium compounds URhGe and UCoGe, as well as the recently discovered UTe₂.
arXiv:2312.02893

The talk is based on works included in doctor of science dissertation.

In this work, we propose a theory for (meta)stable states of Néel-type skyrmions in weak nonuniform magnetic and electrin fields using a novel ansatz for modeling non-symmetric magnetization. Our theory considers changes in skyrmion parameters and deformations from symmetric shapes, simplifying the calculation of skyrmion free energy. By minimizing the free energy in two stages, we can identify stable and metastable states. The theory is employed to study the skyrmion in the stray field of a Pearl vortex. Our methodology reveals how skyrmion parameters depend on the vortex field strength and provides a phase diagram indicating regions with metastable configurations.
arXiv:2311.05578

Motivated by the principles of the conformal bootstrap, primarily the principle of Locality, simultaneously with the requirement of space-time supersymmetry, we reconsider constructions of compactified superstring models. Starting from requirements of space-time supersymmetry and mutual locality, we construct a complete set of physical fields of orbifolds of Gepner models. To technically implement this, we use spectral flow generators to construct all physical fields from the chiral primary fields.

We revisit the classical Goddard Kent Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive formulas for matrix elements of natural vertex operators between these vectors. This leads to relations on conformal blocks. Due to the AGT relation, these relations are equivalent to blowup relations on Nekrasov partition functions with the presence of the surface defect. These relations can be used to prove formulas for the Painlev\'{e} tau-functions (following Nekrasov's method). As another application we prove new Seiberg integral formulas.
Based on joint work with B. Feigin and A. Trufanov

We consider the interaction of inertial waves with geostrophic flow in a fluid rapidly rotating as a whole. In accordance with the experimental conditions [1], we believe that the inertial waves are excited by a source localized in space near the flow boundary and then propagate into the region where a vortex geostrophic flow is present. First, in the approximation of quasi-homogeneity of the geostrophic flow, we consider an evolution of a wave packet of inertial waves. We show that the Doppler effect and the dispersion law of inertial waves lead to the possibility for the wave number of the packet to turn to infinity at a certain point in space. In order to study this process through the analysis of the wave equation, we consider the problem of the propagation of an inertial wave in a time-constant shear flow with straight streamlines. In this problem, there is homogeneity in coordinates along the axis of rotation and along the streamlines of the shear flow, and also in time, which makes it possible to derive a one-dimensional wave equation along the spanwise direction of the shear flow. We show that the absorption of the wave by the shear flow is possible if the spatical wariation of the shear flow exceeds some threshold which is of order of the phase velocity of the wave. The mathematical description of the wave absorption process is equivalent to the quantum mechanical problem of the one-dimensional fall of a particle in a quadratic potential -1/r^2. Based on the constructed analytical picture, we interpret the recently obtained experimental results.