Quantifying spatiotemporal patterns in classical and quantum systems out of equilibrium.

A rich variety of nonequilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in many-body systems of completely different nature. In this work we provide a solution to this problem by adopting a structural complexity measure to quantify spatiotemporal patterns in the time-dependent digital representation of a system. On the basis of very limited amount of data our approach allows us to distinguish different dynamical regimes and define critical parameters in both classical and quantum systems. By the example of the discrete time crystal realized in nonequilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings, which can be considered as a valuable alternative to previous studies based on the calculations of qubit correlation functions.

Heisenberg-exchange-free nanoskyrmion mosaic.

Isotropic Heisenberg exchange naturally appears as the main interaction in magnetism, usually favouring long-range spin-ordered phases. The anisotropic Dzyaloshinskii-Moriya interaction arises from relativistic corrections and is a priori much weaker, even though it may sufficiently compete with the isotropic one to yield new spin textures. In this work, we challenge this well-established paradigm, and propose to explore a Heisenberg-exchange-free magnetic world. In this case, the Dzyaloshinskii-Moriya interaction induces magnetic frustration in two dimensions, from which the competition with an external magnetic field results in a new mechanism producing skyrmions of nanoscale size. A single nanoskyrmion can already be stabilized in a few-atom cluster, and may then be used as LEGO® block to build a large magnetic mosaic. The realization of such topological spin nanotextures in sp- and p -electron compounds or in ultracold atomic gases would open a new route toward robust and compact magnetic memories.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Band filling dependence of the Curie temperature in CrO2.

Rutile CrO2 is an important half-metallic ferromagnetic material, which is also widely used in magnetic recording. In an attempt to find the conditions, which lead to the increase of the Curie temperature (T C), we study theoretically the band-filling dependence of interatomic exchange interactions in the rutile compounds. For these purposes, we use the effective low-energy model for the magnetic t 2g bands, derived from the first-principles electronic structure calculations in the Wannier basis, which is solved by means of dynamical mean-field theory. After the solution, we calculate the interatomic exchange interactions, by using the theory of infinitesimal spin rotations, and evaluate T C. We argue that, as far as the Curie temperature is concerned, the band filling realized in CrO2 is far from being the optimal one and much higher T C can be obtained by decreasing the number of t 2g electrons (n) via the hole doping. We find that the optimal n is close to 1, which should correspond to the case of VO2, provided that it is crystallized in the rutile structure. This finding was confirmed by using the experimental rutile structure for both CrO2 and VO2 and reflects the general tendency towards ferromagnetism for the narrow-band compounds at the beginning of the band filling. In particular, our results suggest that the strong ferromagnetism can be achieved in the thin films of VO2, whose crystal structure is controlled by the substrate.

First-order transition between a small gap semiconductor and a ferromagnetic metal in the isoelectronic alloy FeSi1-xGex.

The contrasting ground states of isoelectronic, isostructural FeSi and FeGe are explained within an extended local density approximation scheme (LDA+U) by an appropriate choice of the Coulomb repulsion U on the Fe sites. A minimal two-band model with interband interactions leads to a phase diagram for the alloys FeSi1-xGex. A mean field approximation gives a first-order transition between a small gap semiconductor and a ferromagnetic metal as a function of magnetic field, temperature, and concentration x. Unusually the transition from metal to insulator is driven by broadening, not narrowing, the bands and it is the metallic state that shows magnetic order.

[The basic principles for the analytical study of epidemic-control measures in the modelling of epidemic processes]. / Osnovnye printsipy analiticheskogo issledovaniia protivoépidemicheskikh meropriiatii pri modelirovanii épidemicheskikh protsessov.

For prognostication of epidemic aerogenic infections with the help of mathematical modeling the authors propose to regard the testing population as a unity of the following streams: susceptible to infection, embraced with emergency vaccination, just vaccinated, protected with the measures of specific or emergency vaccination. Each stream has its own equation which is analogous in its structure to the epidemic dynamics modeling made by O. V. Baroian and L. A. Rvachev, and besides this has correction coefficients which depict the grade of the mobility downtrend due to prophylactic measures. The model built on the bases of the proposed methods makes it possible to determine the level and dynamics of morbidity depending on the volume and efficiency of each sanitary measure described in it.