Induced topological pressure for countable state Markov shifts

We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to important thermodynamical quantities, which are usually given only implicitly by certain identities involving the classically defined pressure. In this context we generalise Savchenko's definition of entropy for special flows to a corresponding notion of topological pressure and show that this new notion coincides with the induced pressure for a large class of H\"older continuous height functions not necessarily bounded away from zero. Secondly, the dependence on the subset of words gives rise to interesting new results connecting the Gurevi{\vc} and the classical pressure with exhausting principles for a large class of Markov shifts. In this context we consider dynamical group extentions to demonstrate that our new approach provides a useful tool to characterise amenability of the underlying group structure.Comment: 28 page

Re-entrant resonant tunneling

We study the effect of electron-electron interactions on the resonant-tunneling spectroscopy of the localized states in a barrier. Using a simple model of three localized states, we show that, due to the Coulomb interactions, a single state can give rise to two resonant peaks in the conductance as a function of gate voltage, G(Vg). We also demonstrate that an additional higher-order resonance with Vg-position in between these two peaks becomes possibile when interactions are taken into account. The corresponding resonant-tunneling process involves two-electron transitions. We have observed both these effects in GaAs transistor microstructures by studying the time evolution of three adjacent G(Vg) peaks caused by fluctuating occupation of an isolated impurity (modulator). The heights of the two stronger peaks exibit in-phase fluctuations. The phase of fluctuations of the smaller middle peak is opposite. The two stronger peaks have their origin in the same localized state, and the third one corresponds to a co-tunneling process.Comment: 9 pages, REVTeX, 4 figure

Magnon caustics in face centered cubic ferromagnets

Caustic phenomenon in magnon propagation picture in face centered cubic lattice is investigated. The employed model takes into account the Heisenberg exchange interaction between an atom's spin and it's nearest and next nearest neighbors. Caustic directions are defined by exploring the corresponding dispersion relations. On the basis of face centered cubic lattice of EuS ferromagnet, such singular peculiarities are investigated for different Heisenberg exchange parameters. Magnon energy regions where the caustics can be observed are defined together with the caustic directions in characteristical crystallographic planes {100} and {110}. It was obtained that caustics can be observed if the magnon frequency is about hundreds of gigahertz, and the widths of the caustic direction regions, that are determined by the magnon frequencies, are of the order of dozens of degrees. © Published under licence by IOP Publishing Ltd.Russian Foundation for Basic Research, RFBR: 18-32-00139Ural Branch, Russian Academy of Sciences, UB RAS: No.18-10-2-37The research was carried out within the state assignment of FASO of Russia (theme “Function” AAAA-A19-119012990095-0), supported by RFBR (project No. 18-32-00139), and by UB RAS Project No.18-10-2-37

The possible subjects with public authority in european countries

This study was aimed at analyzing the constitutional consolidation of the oath in the states of Eastern Europe, using various criteri