Stability of atoms in the Brown-Ravenhall model

We consider the Brown--Ravenhall model of a relativistic atom with N electrons and a nucleus of charge Z and prove the existence of an infinite number of discrete eigenvalues for N <= Z. As an intermediate result we prove a HVZ-type theorem for these systems.Comment: 31 pages, accepted to "Annales Henry Poincare". The error in Lemma 3 of the previous version is corrected and the corresponding changes are done in the proof of Theorem

Lieb–Thirring and Cwickel–Lieb–Rozenblum inequalities for perturbed graphene with a Coulomb impurity

We study the two dimensional massless Coulomb–Dirac operator restricted to its positive spectral subspace and prove estimates on the negative eigenvalues created by electromagnetic perturbations

Multiparticle Brown-Ravenhall operators in external fields

The Brown–Ravenhall model is used in quantum physics and chemistry to describe relativistic multiparticle systems, particularly atoms and molecules. In this dissertation we analyse some general properties of this model on the mathematically rigorous level. We show that under very general assumptions on the interaction potentials the essential spectrum of multiparticle Brown–Ravenhall operators is the right semiaxis starting from the minimal energy possible for the decompositions of the system into two clusters. This result, usually called HVZ theorem, is the fundamental starting point in the spectral analysis of multiparticle Hamiltonians with decaying potentials. Suppose now that the particles constituting the system repel each other but are confined by an external field decaying at infinity. In this situation we prove that the eigenfunctions corresponding to the eigenvalues below the essential spectrum decay exponentially. If some particles of the system are identical, the laws of quantum mechanics often require to reduce the operator to the subspace of functions which transform according to some irreducible representation of the group of permutation of identical particles. On the other hand, the interactions are often invariant under some rotations and reflections. We prove that both the HVZ theorem and the exponential decay of eigenfunctions hold true for operators reduced to the irreducible representations of the above groups. Our results are potentially important in further studies of the spectrum and in the scattering theory of Brown–Ravenhall operators

“Distant” Communication: Transformation of Interaction Between Russian Society and Authorities in the Era of the Global Pandemic

Introduction. The article is devoted to the identification and analysis of the dominant trends in the transformation of forms and technologies of communication used by the government and Russian society institutions in the context of the COVID-19 spread. The attention is focused on the characteristics of socio-political factors that determine the level of trust/distrust of citizens and representatives of various social groups to intentions and actions of the authorities and administration at the federal, regional and municipal levels in the Russian Federation to overcome the consequences of the global pandemic in the process of communication. Methods. The communicative practices of public and civil institutions are revealed in the context of interpreting the specifics of the existing public space and public policy of modern Russia. The theoretical and methodological basis of the research are the political-communicative and action-activist approaches, the spatial dimension of political processes principles, which make it possible to rely on the systemic vision of the information and discursive, practical and management elements of the multidimensional concept of public policy. The work uses the methods of political comparative studies, forecasting, interpretation of empirical data obtained by leading Russian and foreign research centers, as well as by the authors in the framework of their grant research. Results. An attempt was made to conduct political analysis of the dominant negative and positive factors revealing the specifics of the COVID-19 spread in the Russian Federation from the point of view of the everyday practices of modern Russian society and the consolidated institutional system of public administration. The authors trace the link between the situation of uncertainty resulting from the spread of the global threat, the desire to ensure international and national security, as well as the transformation of forms and technologies of communication between citizens, public institutions, the state. The real and potential resources of communication between society and the authorities for building an effective system to minimize the negative consequences of the pandemic for representatives of various socio-demographic, professional, and status-role groups, that are included in the structures of discussion, decision-making and implementation, are highlighted. The results of theoretical and empirical studies revealing a public opinion on the impact of COVID-19 on the socio-political process in modern Russia are interpreted. Discussion. The question of the forms and technologies of communication between the actors of modern public policy in the significant decisions making process in the context of strengthening destructive factors and the institutionalization of a “riskgenerating” society remains poorly studied

Microscopic Analysis of Severe Structural Rearrangements of the Plant Endoplasmic Reticulum and Golgi Caused by Overexpression of Poa semilatent virus Movement Protein

Cell-to-cell transport of plant viruses is mediated by virus-encoded movement proteins and occurs through plasmodesmata interconnecting neighboring cells in plant tissues. Three movement proteins coded by the “triple gene block” (TGB) and named TGBp1, TGBp2 and TGBp3 have distinct functions in viral transport. TGBp1 binds viral genomic RNAs to form ribonucleoprotein complexes representing the transport form of viral genome, while TGBp2 and TGBp3 are necessary for intracellular delivery of such complexes to plasmodesmata. Recently, it was revealed that overexpression of Potato virus X TGBp3 triggers the unfolded protein response mitigating the endoplasmic reticulum (ER) stress leading to cell death if this protein reaches high levels in the ER. Here we report microscopic studies of the influence of the Poa semilatent hordeivirus TGBp3 overexpressed in Nicotiana benthamiana epidermal cells by particle bombardment on cell endomembranes and demonstrate that the protein C-terminal transmembrane segment contains a determinant responsible for vesiculation and coalescence of the endoplasmic reticulum and Golgi presumably accompanying the ER stress that can be induced upon high-level TGBp3 expression