The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi–dimensional Hamiltonian systems. We propose an efficient computation of the GALIk indices, which represent volume elements of k randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algori...

In Ref. [1] Hořava suggested, that the multi-fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the 3+1 D system and concentrate on the particular ca...

Active Galactic Nuclei are considered as possible sites of cosmic ray acceleration and some of them have been observed as high energy gamma ray emitters (Blazars). There naturally comes an appealing idea that the acceleration of the highest energy cosmic rays in the AGNs has a signature in the form of gamma ray emission and high energy neutrino emission through the collisions of very high energ...

We place the Thomas-Fermi-von Weizsacker model of atoms on a firm mathematical footing. We prove existence and uniqueness of solutions of the Thomas-Fermi-von Weizsacker equation as well as the fact that they minimize the Thomas-Fermi-von Weizsacker energy functional. Moreover, we prove the existence of binding for two very dissimilar atoms in the frame of this model. Introduction The Thomas-Fe...

The full Klein-Nishina cross section for the inverse Compton scattering interactions of electrons implies a significant reduction of the electron energy loss rate compared to the Thomson limit when the electron energy exceeds the critical Klein-Nishina energy E K = γ K m e c 2 = 0.27m 2 e c 2 /(k B T), where T denotes the temperature of the photon graybody distribution. As a consequence the tot...

The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss interesting dynamics of the energy transfer process starting from a large-scale excitation. This failure is traced to an enforcement of the exact resonance conditi...

We reconsider the problem of the anomalous Hall effect in ferromagnetic SrRuO3, incorporating insights from the recently developed theory of Weyl semimetals. We demonstrate that SrRuO3 possesses a large number of Weyl nodes, separated in momentum space, in its bandstructure. While the nodes normally do not coincide with the Fermi energy, unless the material is doped, we show that even the nodes...

We report angle-resolved photoelectron spectroscopy results of the Fermi surface of Ca1.5Sr0.5RuO4, which is at the boundary of magnetic/orbital instability in the phase diagram of the Ca-substituted Sr ruthenates. Three t(2g) energy bands and the corresponding Fermi surface sheets are observed, which are also present in the Ca-free Sr2RuO4. We find that while the Fermi surface topology of the ...

We test a non-equilibrium approach to study the behaviour of a Bose–Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree–Fock–Bogoliubov (HFB) equations of motion for the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. Howe...

A hallmark of Weyl semimetal is the existence of surface Fermi arcs. An intriguing question is what determines the connectivity of surface Fermi arcs, when multiple pairs of Weyl nodes are present. To answer this question, we show that the locations of surface Fermi arcs are predominantly determined by the condition that the Zak phase integrated along the normal-to-surface direction is . The Za...