Hyperbolic Topological Invariants and the Black Hole Geometry

We discuss the isometry group structure of three-dimensional black holes and Chern-Simons invariants. Aspects of the holographic principle relevant to black hole geometry are analyzed.Comment: 11 pages, AMSTeX, Contribution to the Fifth Alexander Friedmann International Seminar on Gravitation and Cosmolog

Analytical device model for graphene bilayer field-effect transistors using weak nonlocality approximation

We develop an analytical device model for graphene bilayer field-effect transistors (GBL-FETs) with the back and top gates. The model is based on the Boltzmann equation for the electron transport and the Poisson equation in the weak nonlocality approximation for the potential in the GBL-FET channel. The potential distributions in the GBL-FET channel are found analytically. The source-drain current in GBL-FETs and their transconductance are expressed in terms of the geometrical parameters and applied voltages by analytical formulas in the most important limiting cases. These formulas explicitly account for the short-gate effect and the effect of drain-induced barrier lowering. The parameters characterizing the strength of these effects are derived. It is shown that the GBL-FET transconductance exhibits a pronounced maximum as a function of the top-gate voltage swing. The interplay of the short-gate effect and the electron collisions results in a nonmonotonic dependence of the transconductance on the top-gate length.Comment: 12 pages, 7 figure

Fuzzy interpretation for temporal-difference learning in anomaly detection problems

Nowadays, information control systems based on databases develop dynamically worldwide. These systems are extensively implemented into dispatching control systems for railways, intrusion detection systems for computer security and other domains centered on big data analysis. Here, one of the main tasks is the detection and prediction of temporal anomalies, which could be a signal leading to significant (and often critical) actionable information. This paper proposes the new anomaly prevent detection technique, which allows for determining the predictive temporal structures. Presented approach is based on a hybridization of stochastic Markov reward model by using fuzzy production rules, which allow to correct Markov information based on expert knowledge about the process dynamics as well as Markov’s intuition about the probable anomaly occurring. The paper provides experiments showing the efficacy of detection and prediction. In addition, the analogy between new framework and temporal-difference learning for sequence anomaly detection is graphically illustrated.Web of Science64363262

Anisotropic Topological Hall Effect with Real and Momentum Space Berry Curvature in the Antiskrymion Hosting Heusler Compound Mn1.4_{1.4}PtSn

The topological Hall effect (THE) is one of the key signatures of topologically non-trivial magnetic spin textures, wherein electrons feel an additional transverse voltage to the applied current. The magnitude of THE is often small compared to the anomalous Hall effect. Here, we find a large THE of 0.9 $\mu\Omega$cm that is of the same order of the anomalous Hall effect in the single crystalline antiskyrmion hosting Heusler compound Mn$_{1.4}$PtSn, a non-centrosymmetric tetragonal compound. The THE is highly anisotropic and survives in the whole temperature range where the spin structure is noncoplanar (<170 K). The THE is zero above the spin reorientation transition temperature of 170 K, where the magnetization will have a collinear and ferromagnetic alignment. The large value of the THE entails a significant contribution from the momentum space Berry curvature along with real space Berry curvature, which has never been observed earlier

Modifications of gravity via differential transformations of field variables

We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFT) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process the dynamics of the theory might either change or conserve. After that we concentrate on the theories of gravity which appear as a result of various DFT applied to general relativity, namely the mimetic gravity and Regge-Teitelboim embedding theory. We review main results related to the extension of dynamics in these theories, as well as the possibility to write down the action of a theory after DFT as the action of the original theory before DFT plus an additional term. Such a term usually contains some constraints with Lagrange multipliers and can be interpreted as an action of additional matter, which might be of use in cosmological applications, e.g. for the explanation of the effects of dark matter.Comment: 18 page

Robust metastable skyrmions with tunable size in the chiral magnet FePtMo3_3N

Synthesis of new materials that can host magnetic skyrmions and their thorough experimental and theoretical characterization are essential for future technological applications. The $\beta$-Mn-type compound FePtMo$_3$N is one such novel material that belongs to the chiral space group $P4_132$, where the antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of inversion symmetry. We report the results of small-angle neutron scattering (SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground state is a long-period spin helix with a Curie temperature of 222~K. The magnetic field-induced redistribution of the SANS intensity showed that the helical structure transforms to a lattice of skyrmions at $\sim$13~mT at temperatures just below $T_{\text C}$. Our key observation is that the skyrmion state in FePtMo$_3$N is robust against field cooling down to the lowest temperatures. Moreover, once the metastable state is prepared by field cooling, the skyrmion lattice exists even in zero field. Furthermore, we show that the skyrmion size in FePtMo$_3$N exhibits high sensitivity to the sample temperature and can be continuously tuned between 120 and 210~nm. This offers new prospects in the control of topological properties of chiral magnets.Comment: 6 pages, 4 figure