arXiv subjects

A. Davydov

Publications and source records attributed to A. Davydov.

6 recordsLinked to original sources

arXiv2020

Ab initio theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms

We extend the two leading methods for the \emph{ab initio} computational descrip tion of phonon-mediated superconductors, namely Eliashberg theory and density fu nctional theory for superconductors (SCDFT), to include plasmonic effects. Furth ermore, we introduce a hybrid formalism in which the Eliashberg approximation fo r the electron-phonon coupling is combined with the SCDFT treatment of the dynam ically screened Coulomb interaction. The methods have been tested on a set of we ll-known conventional superconductors by studying how the plasmon contribution a ffects the phononic mechanism in determining the critical temperature (\tc). Our simulations show that plasmonic SCDFT leads to a good agreement between predict ed and measured \tc's, whereas Eliashberg theory considerably overestimates the plasmon-mediated pairing and, therefore, \tc. The hybrid approach, on the other hand, gives results close to SCDFT and overall in excellent agreement with exper iments.

cond-mat.supr-con↗

arXiv2018

Casimir (vacuum) energy in planar QED with strong coupling

The essentially non-perturbative vacuum polarization effects, caused by an extended external supercritical Coulomb source, are explored for a planar Dirac-Coulomb (DC) system with strong coupling (similar to graphene and graphene-based heterostructures). Taking account of results, obtained in \cite{partI2018} for the induced charge density $ρ_{VP}(\vec{r})$, in the present paper the evaluation of the Casimir (vacuum) energy $\mathcal{E}_{VP}$ is presented. The main result is that for a wide range of the system parameters in the overcritical region $\mathcal{E}_{VP}$ turns out to be a rapidly decreasing negative function $\sim - Z^3/R_0\, $ with $Z\, , R_0$ being the charge and the size of the external source. By an explicit calculation the possibility for complete screening of the electrostatic reflection self-energy of the external source by such polarization effects for $Z \gg Z_{cr,1}$ is demonstrated. The dependence of the Casimir energy on the screening of the Coulomb asymptotics of the external source at some $R_1>R_0$ is also explored in detail, and some peculiar effects in the partial channels with the lowest rotational numbers $m_j=\pm 1/2\, , \pm3/2$ in the screened case are also discussed.

cond-mat.mes-hall↗

arXiv2018

Essentially non-perturbative and peculiar polarization effects in planar QED with strong coupling

The essentially non-perturbative polarization effects are considered for a planar supercritical Dirac-Coulomb system with strong coupling (similar to graphene and graphene-based heterostructures) in terms of induced charge density $ρ_{VP}(\vec{r})$. The main attention is paid to the renormalization, convergence of the partial expansion and the behavior of $ρ_{VP}(\vec{r})$ and the integral induced charge $Q_{VP}$ in the overcritical region. The dependence of the induced density on the screening of the Coulomb asymptotics of the external source is also explored in detail. Some peculiar effects in the discrete spectrum with the lowest rotational numbers $m_j=\pm 1/2\, , \pm3/2$ in the screened case are detected and their possible role in the transition through corresponding $Z_{cr}$ is also discussed.

cond-mat.mes-hall↗

arXiv2014

Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds

We describe the group of braided tensor autoequivalences of the Drinfeld centre of a finite group $G$ isomorphic to the identity functor (just as a functor) as a semi-direct product $Aut^1_{br}(\Z(G))\ \simeq\ Out_{2-cl}(G)\ltimes B(G)\ $ of the group of double class preserving automorphisms and the Bogomolov multiplier of $G$. The Bogomolov multiplier $B(G)$ is the subgroup of its Schur multiplier $H^2(G,k^*)$ of classes vanishing on abelian subgroups of $G$. We show that elements of $Aut^1_{br}(\Z(G))$ give rise to different realisations of the charge conjugation modular invariant for $G$-orbifolds of holomorphic conformal field theories.

math.CT↗

arXiv2000

Pentagon equation and matrix bialgebras

We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the non-unitary case. We establish the relation between Hopf-Galois algebras and solutions to modified pentagon equation.

math.QA↗

arXiv2000

Finite groups with the same character tables, Drinfel'd algebras and Galois algebras

We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations of class-preserving automorphisms and permutation representations with the same character in terms of Drinfel'd algebras are also given.

math.RT↗