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Few-Shot Adversarial Learning of Realistic Neural Talking Head ModelsMay 20 2019Several recent works have shown how highly realistic human head images can be obtained by training convolutional neural networks to generate them. In order to create a personalized talking head model, these works require training on a large dataset of ... More

Learnable Triangulation of Human PoseMay 14 2019We present two novel solutions for multi-view 3D human pose estimation based on new learnable triangulation methods that combine 3D information from multiple 2D views. The first (baseline) solution is a basic differentiable algebraic triangulation with ... More

Fractional Quantum Hall Effect and Featureless Mott InsulatorsNov 20 2009Mar 11 2010We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we demonstrate ... More

Topological SemimetalsOct 25 2016Topological semimetals and metals have emerged as a new frontier in the field of quantum materials. Novel macroscopic quantum phenomena they exhibit are not only of fundamental interest, but may hold some potential for technological applications.

The existential fragment of S1S over element and successor is the co-Buchi languagesJan 20 2014Buchi's theorem, in establishing the equivalence between languages definable in S1S over element and < and the omega-regular languages also demonstrated that S1S over element and < is no more expressive than its existential fragment. It is also easy to ... More

Andreev-Bashkin effect and knot solitons in interacting mixture of a charged and a neutral superfuids with possible releveance for neutron starsNov 15 2002Sep 29 2004We discuss a mixture of interacting a neutral and a charged Bose condensates, which is supposed being realized in interior of neutron stars in form of coexistent neutron superfluid and protonic superconductor. We show that in this system, besides ordinary ... More

Characteristic length scales and formation of vortices in the Abelian Higgs model in the presence of a uniform background chargeSep 28 2000May 23 2001In this brief report we consider a non-local Abelian Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices which key feature is a strong radial electric field. We estimate the basic properties ... More

Unconventional rotational responses of hadronic superfluids in a neutron star caused by strong entrainment and a $Σ^-$ hyperon gapJan 28 2009Nov 17 2009I show that the usual model of the rotational response of a neutron star, which predicts rotation-induced neutronic vortices and no rotation-induced protonic vortices, does not hold (i) beyond a certain threshold of entrainment interaction strength nor ... More

The Hofer norm of a contactomorphismNov 06 2014Oct 21 2015We show that the $L^{\infty}$-norm of the contact Hamiltonian induces a non-degenerate right-invariant metric on the group of contactomorphisms of any closed contact manifold. This contact Hofer metric is not left-invariant, but rather depends naturally ... More

Electing a committee with constraintsFeb 15 2019We consider the problem of electing a committee of $k$ candidates, subject to some constraints as to what this committee is supposed to look like. In our framework, the pool of candidates is divided into tribes, and constraints of the form "at least $p$ ... More

On the Hofer-Zehnder conjectureMay 12 2019We prove that if a Hamiltonian diffeomorphism on a closed monotone symplectic manifold with semisimple quantum homology has a finite number of contractible periodic points then the sum of the ranks of the local Floer homologies at its contractible fixed ... More

Aspects of topology of condensates and knotted solitons in condensed matter systemsSep 28 2000Jun 08 2001The knotted solitons introduced by Faddeev and Niemi is presently a subject of great interest in particle and mathematical physics. In this paper we give a condensed matter interpretation of the recent results of Faddeev and Niemi.

Nonlinear sigma model approach for phase disorder transitions and the pseudogap phase in chiral Gross-Neveu, Nambu-Jona-Lasinio models and strong-coupling superconductorsSep 09 1999May 23 2001We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross-Neveu and the modified Nambu-Jona-Lasinio models at low $N$ and condensation from pseudogap phase in strong-coupling ... More

Two statements of the Duggan-Schwartz theoremNov 21 2016The Duggan-Schwartz theorem (Duggan and Schwartz, 1992) is a famous result concerning strategy-proof social choice correspondences, often stated as "A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak ... More

Grammars and reinforcement learning for molecule optimizationNov 27 2018We seek to automate the design of molecules based on specific chemical properties. Our primary contributions are a simpler method for generating SMILES strings guaranteed to be chemically valid, using a combination of a new context-free grammar for SMILES ... More

Symmetries of polytopes with fixed edge lengthsAug 28 2018We consider an interesting class of combinatorial symmetries of polytopes which we call \emph{edge-preserving symmetries}. These symmetries not only preserve the combinatorial structure of a polytope but also map each edge of the polytope to an edge of ... More

Chiral anomaly without relativityOct 26 2015Perspectives article on J. Xiong et al., Science 350, 413 (2015).

Topological response in ferromagnetsDec 31 2013Apr 04 2014We present a theory of the intrinsic anomalous Hall effect in a model of a doped Weyl semimetal, which serves here as the simplest toy model of a generic three-dimensional metallic ferromagnet with Weyl nodes in the electronic structure. We analytically ... More

Chiral Anomaly and Diffusive Magnetotransport in Weyl MetalsAug 29 2014Dec 09 2014We present a microscopic theory of diffusive magnetotransport in Weyl metals and clarify its relation to chiral anomaly. We derive coupled diffusion equations for the total and axial charge densities and show that chiral anomaly manifests as a magnetic-field-induced ... More

Anomalous Hall Effect in Weyl MetalsJun 11 2014Oct 29 2014We present a theory of the anomalous Hall effect (AHE) in a doped Weyl semimetal, or Weyl metal, including both intrinsic and extrinsic (impurity scattering) contributions. We demonstrate that a Weyl metal is distinguished from an ordinary ferromagnetic ... More

Chiral anomaly and transport in Weyl metalsFeb 26 2015We present an overview of our recent work on transport phenomena in Weyl metals, which may be connected to their nontrivial topological properties, particularly to chiral anomaly. We argue that there are two basic phenomena, which are related to chiral ... More

Phase diagram of planar U(1)xU(1) superconductors: condensation of vortices with fractional flux and a superfluid stateJan 30 2002Apr 04 2004We discuss a phase diagram of two-dimentional $U(1)\times U(1)$ superconductor in the field theoretic formalizm of Ref. [17]. In particular we discuss that in the type-I case the system exhibit a quasi-neutral quasi-superfluid state.

Non-Meissner electrodynamics and knotted solitons in two-component superconductorsSep 25 2008Feb 15 2009I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in ... More

Thermodynamics of Crossover from Weak- to Strong-Coupling SuperconductivityOct 05 2000May 23 2001In this paper we study an evolution of low-temperature thermodynamical quantities for an electron gas with a $ \delta $-function attraction as the system crosses over from weak-coupling (BCS-type) to strong-coupling (Bose-type) superconductivity in three ... More

Remarks on invariants of hamiltonian loopsMay 11 2009Jun 25 2009In this note the interrelations between several natural morphisms on the $\pi_1$ of groups of Hamiltonian diffeomorphisms are investigated. As an application, the equality of the (non-linear) Maslov index of loops of quantomorphisms of prequantizations ... More

Dual neutral variables and knot solitons in triplet superconductorsJun 18 2001Apr 19 2002In this paper we derive a dual presentation of free energy functional for spin-triplet superconductors in terms of gauge-invariant variables. The resulting equivalent model in ferromagnetic phase has a form of a version of the Faddeev model. This allows ... More

Generalized problem of ApolloniusNov 06 2016Theorem. Given four various generalized circles on a plane and they don't touch in the same point. Then there are at most six generalized circles such that each of them touches each of the given. This theorem is a generalization of the famous problem ... More

Proof of Radon's theorem by lowering the dimensionMar 25 2019There is the classical Radon theorem. Given integer $d \geq 1$ and $d+2$ points in d-dimensional space $R^d$. Then these points can be divided into two disjoint subsets whose convex hulls have a non-empty intersection. The original proof of this theorem ... More

Pseudorotations and Steenrod squaresMay 13 2019In this note we prove that if a closed monotone symplectic manifold $M$ of dimension $2n,$ satisfying a homological condition, that holds in particular when the minimal Chern number is $N>n,$ admits a Hamiltonian pseudorotation, then the quantum Steenrod ... More

Groups normalized by the odd unitary groupFeb 22 2019Mar 01 2019We will give a definition of quadratic forms on bimodules and prove the sandwich classification theorem for subgroups of the general linear group $\mathrm{GL}(P)$ normalized by the elementary unitary group $\mathrm{EU}(P)$ if $P$ is a nondegenerate bimodule ... More

Fractional-flux vortices and spin superfluidity in triplet superconductorsApr 03 2004Feb 28 2005We discuss a novel type of fractional flux vortices along with integer flux vortices in Kosterlitz-Thouless transitions in a triplet superconductor. We show that under certain conditions a spin-triplet superconductor should exhibit a novel state of {\it ... More

Neither a type-I nor a type-II superconductivity in a two-gap systemFeb 12 2003Nov 26 2004We show that in two-gap Ginzburg-Landau model there is a wide range of parameters where the behaviour of the superconductor in external field can not be classified nor as type-I nor as type-II. In this regime the superconductor features a nonmonotonic ... More

Mass generation without phase coherence in the Chiral Gross-Neveu Model at finite temperature and small N in 2+1 dimensionsJul 13 1999Aug 15 2000The chiral Gross-Neveu model is one of the most popular toy models for QCD. In the past, it has been studied in detail in the large-N limit. In this paper we study its small-N behavior at finite temperature in 2+1 dimensions. We show that at small N the ... More

Cake Cutting MechanismsMar 01 2012Apr 07 2012We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated by the allocations ... More

The Jordan constant for Cremona group of rank 2Oct 30 2016We compute the Jordan constant for the group of birational automorphisms of a projective plane $\mathbb{P}^2_{\mathbb k}$, where ${\mathbb k}$ is either an algebraically closed field of characteristic 0, or the field of real numbers, or the field of rational ... More

Electing a committee with constraintsFeb 15 2019Feb 21 2019We consider the problem of electing a committee of $k$ candidates, subject to some constraints as to what this committee is supposed to look like. In our framework, the pool of candidates is divided into tribes, and constraints of the form "at least $p$ ... More

The Dynamical equations for $\mathfrak{gl}(n\vert m)$Mar 28 2019In this note we propose a compatible set of equations which commutes with the Knizhnik-Zamolodchikov equations based on the $\mathfrak{{gl}}(n\vert m)$ symmetry algebra and establish the Matsuo-Cherednik correspondence for them.

A `converse' to the Constraint LemmaMar 21 2019The main result is a direct proof of the implication $(LVKF_{k,3})\Rightarrow( LT_{3k-1,3})$ below. Consider the following statements: ($LVKF_{1,3}$) From any 11 points in $ \mathbb{R}^{3}$ one can choose 3 pairwise disjoint triples whose convex hulls ... More

Vortex matter and generalizations of dipolar superfluidity concept in layered systemsNov 15 2006Oct 28 2007In the first part of this letter we discuss electrodynamics of an excitonic condensate in a bilayer. We show that under certain conditions the system has a dominant energy scale and is described by the effective electrodynamics with "planar magnetic charges". ... More

A marginal remark on massless neutral boson is two-gap superconductorsJan 28 2002Feb 04 2004We make some remarks on massless neutral boson in two-flavour Abelian Higgs model. {\bf Note added:} {\it this remark was merged with journal version of cond-mat/0111192 on a referee request.}

Vortices with fractional flux in two-gap superconductors and in extended Faddeev modelNov 12 2001Sep 03 2002We discuss vortices allowed in two-gap superconductors, bilayer systems and in equivalent extended Faddeev model. We show that in these systems there exist vortices which carry an arbitrary fraction of magnetic flux quantum. Besides that we discuss topological ... More

Nonlinear sigma model approach for chiral fluctuations and symmetry breakdown in Nambu-Jona-Lasinio modelJun 09 2000In this paper we discuss symmetry breakdown in NJL model at low N_c. In particular we propose a modified NJL model that displays a symmetry breakdown and also at finite temperatures under certain conditions the chiral fluctuations in this model give rise ... More

Enlacements asymptotiques revisitésNov 06 2014We give an alternative proof of a theorem of Gambaudo-Ghys and Fathi on the interpretation of the Calabi homomorphism for the standard symplectic disc as an average rotation number. This proof uses only basic complex analysis.

The Action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structuresMay 29 2011Feb 21 2012We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound on the symplectic ... More

Stability of Superflow for Ultracold Fermions in Optical LatticesFeb 14 2008Apr 07 2008Motivated by recent observations of superfluidity of ultracold fermions in optical lattices, we investigate the stability of superfluid flow of paired fermions in the lowest band of a strong optical lattice. For fillings close to one fermion per site, ... More

Vortex-Peierls States in Optical LatticesFeb 12 2006May 10 2006We show that vortices, induced in cold atom superfluids in optical lattices, may order in a novel vortex-Peierls ground state. In such a state vortices do not form a simple lattice but arrange themselves in clusters, within which the vortices are partially ... More

Weyl Semimetal in a Topological Insulator MultilayerMay 25 2011Sep 16 2011We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. ... More

Superfluid-Insulator Transitions on the Triangular LatticeJun 18 2005We report on a phenomenological study of superfluid to Mott insulator transitions of bosons on the triangular lattice, focusing primarily on the interplay between Mott localization and geometrical charge frustration at 1/2-filling. A general dual vortex ... More

Multiband superfluidity and superfluid to band-insulator transition of strongly interacting fermions in an optical latticeFeb 06 2009We study the multiband superfluid and the superfluid (SF) to band insulator (BI) transition of strongly interacting fermionic atoms in an optical lattice at a filling of two fermions per well. We present physical arguments to show that a consistent mean ... More

Spin Relaxation in a Two-Dimensional Electron Gas in a Perpendicular Magnetic FieldJan 21 2004We consider the problem of spin relaxation in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field. We assume that the spin relaxation is induced by the Rashba spin-orbit (SO) interaction, which appears due to the inversion asymmetry ... More

Anomalous Hall Effect in Ferromagnetic Semiconductors in the Hopping Transport RegimeFeb 27 2003Jul 30 2003We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous ... More

An Approximate Subgame-Perfect Equilibrium Computation Technique for Repeated GamesFeb 08 2010This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in discounted repeated games. The process starts with a single hypercube approximation of the set of SPE. Then the initial hypercube is ... More

Textured Neural AvatarsMay 21 2019We present a system for learning full-body neural avatars, i.e. deep networks that produce full-body renderings of a person for varying body pose and camera position. Our system takes the middle path between the classical graphics pipeline and the recent ... More

Rotational response of superconductors: magneto-rotational isomorphism and rotation-induced vortex latticeNov 20 2013Mar 03 2014The analysis of nonclassical rotational response of superfluids and superconductors was performed by Onsager (in 1949) \cite{Onsager} and London (in 1950) \cite{London} and crucially advanced by Feynman (in 1955) \cite{Feynman}. It was established that, ... More

EGuaranteeNash for Boolean Games is NEXP-HardDec 15 2013Boolean games are an expressive and natural formalism through which to investigate problems of strategic interaction in multiagent systems. Although they have been widely studied, almost all previous work on Nash equilibria in Boolean games has focused ... More

Bounds on spectral norms and barcodesOct 23 2018We investigate the relations between algebraic structures, spectral invariants, and persistence modules, in the context of monotone Lagrangian Floer homology with Hamiltonian term. Firstly, we use the newly introduced method of filtered continuation elements ... More

Superfluid drag in the two-component Bose-Hubbard modelJan 09 2018In multicomponent superfluids and superconductors, co- and counter-flows of components have in general different properties. It was discussed in 1975 by Andreev and Bashkin, in the context of He$^3$/He$^4$ superfluid mixtures, that inter-particle interactions ... More

Robustness against Power is PSPACE-completeApr 28 2014Power is a RISC architecture developed by IBM, Freescale, and several other companies and implemented in a series of POWER processors. The architecture features a relaxed memory model providing very weak guarantees with respect to the ordering and atomicity ... More

Regularity of linear and polynomial images of Skorohod differentiable measuresJul 01 2019In this paper we study the regularity properties of linear and polynomial images of Skorohod differentiable measures. Firstly, we obtain estimates for the Skorohod derivative norm of a projection of a product of Scorohod differentiable measures. In the ... More

The $L^p$-diameter of the group of area-preserving diffeomorphisms of $S^2$Apr 23 2016Jul 07 2016We show that for each $p \geq 1,$ the $L^p$-metric on the group of area-preserving diffeomorphisms of the two-sphere has infinite diameter. This solves the last open case of a conjecture of Shnirelman from 1985. Our methods extend to yield stronger results ... More

Lagrangian cobordism and metric invariantsNov 27 2015We introduce new pseudo-metrics on spaces of Lagrangian submanifolds of a symplectic manifold $(M,\omega)$ by considering areas associated to projecting Lagrangian cobordisms in $\mathbb{C} \times M$ to the "time-energy plane" $\mathbb{C}$. We investigate ... More

Domain walls and their experimental signatures in s+is superconductorsAug 14 2013Jan 09 2014Arguments were recently advanced that hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ exhibits $s+is$ state at certain doping. Spontaneous breaking of time reversal symmetry in $s+is$ state, dictates that it possess domain wall excitations. Here, we discuss what ... More

Properties of skyrmions and multi-quanta vortices in chiral $p$-wave superconductorsJul 16 2015Apr 20 2016Chiral $p$-wave superconducting state supports a rich spectrum of topological excitations different from those in conventional superconducting states. Besides domain walls separating different chiral states, chiral $p$-wave state supports both singular ... More

Vortex chains due to nonpairwise interactions and field-induced phase transitions between states with different broken symmetry in superconductors with competing order parametersNov 24 2014Jan 20 2015We study superconductors with two order components and phase separation driven by intercomponent density-density interaction, focusing on the phase where only one condensate has non-zero ground-state density and a competing order parameter exists only ... More

Resonant-state expansion for planar photonic-crystal structuresAug 19 2019We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in photonic-crystal structures ... More

Probabilistic hypergraph grammars for efficient molecular optimizationJun 05 2019We present an approach to make molecular optimization more efficient. We infer a hypergraph replacement grammar from the ChEMBL database, count the frequencies of particular rules being used to expand particular nonterminals in other rules, and use these ... More

On the peripheral spectrum of positive elementsMay 17 2017We investigate the peripheral spectrum of irreducible positive elements of an ordered Banach algebra. In particular, we give conditions under which the peripheral spectrum contains (or coincides with) the cyclic group generated by a root of unity, and ... More

Besov classes on finite- and infinite-dimensional spaces and embedding theoremsNov 05 2017We give a new description of classical Besov spaces in terms of a new modulus of continuity. Then a similar approach is used to introduce Besov classes on an infinite-dimensional space endowed with a Gaussian measure.

Collective modes and superflow instabilities of strongly correlated Fermi superfluidsApr 29 2009Oct 29 2009We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated s-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the ... More

Pair density wave instability and Cooper pair insulators in gapped fermion systemsJul 14 2010By analyzing simple models of fermions in lattice potentials we argue that the zero-temperature pairing instability of any ideal band-insulator occurs at a finite momentum. The resulting supersolid state is known as "pair density wave". The pairing momentum ... More

Z_2 and Chiral Anomalies in Topological Dirac SemimetalsJun 27 2016Sep 22 2016We demonstrate that topological Dirac semimetals, which possess two Dirac nodes, separated in momentum space along a rotation axis and protected by rotational symmetry, exhibit an additional quantum anomaly, distinct from the chiral anomaly. This anomaly, ... More

Finite Momentum Pairing Instability of Band-Insulators With Multiple BandsJun 12 2009Jun 08 2012We show, based on microscopic models, that fermionic band insulators with multiple bands and strong interband attraction are generically unstable towards nonzero momentum Cooper pairing leading to a pair density wave (PDW) superfluid state. Our first ... More

On the $L^p$-geometry of autonomous Hamiltonian diffeomorphisms of surfacesMay 30 2014Jun 16 2014We prove a number of results on the interrelation between the $L^p$-metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms ... More

On the large-scale geometry of the L^p-metric on the symplectomorphism group of the two-sphereApr 25 2013Jun 15 2014We prove that the vector space R^d of any finite dimension d with the standard metric embeds in a bi-Lipschitz way into the group of area-preserving diffeomorphisms G of the two-sphere endowed with the L^p-metric for p>2. Along the way we show that the ... More

Binary Sequences with Minimum Peak Sidelobe Level up to Length 68Dec 20 2012Results of an exhaustive search for minimum peak sidelobe level binary sequences are presented. Several techniques for efficiency implementation of search algorithm are described. A table of number of non-equivalent optimal binary sequences with minimum ... More

The $\mathbb{Z}/(p)$-equivariant product-isomorphism in fixed point Floer cohomologyMay 09 2019Let $p \geq 2$ be a prime, and $\mathbb{F}_p$ be the field with $p$ elements. Extending a result of Seidel for $p=2,$ we construct an isomorphism between the Floer cohomology of an exact or Hamiltonian symplectomorphism $\phi,$ with $\mathbb{F}_p$ coefficients, ... More

Classification of ground states and normal modes for phase-frustrated multicomponent superconductorsJun 13 2013Jan 23 2014We classify ground states and normal modes for $n$-component superconductors with frustrated intercomponent Josephson couplings, focusing on $n = 4$. The results should be relevant not only to multiband superconductors, but also to Josephson-coupled multilayers ... More

Twisted and untwisted K-theory quantization, and symplectic topologyAug 27 2015A prequantization space $(P,\alpha)$ is a principal $S^1$-bundle with a connection one-form $\alpha$ over a symplectic manifold $(M,\omega),$ with curvature given by the symplectic form. In particular $\alpha$ is a contact form. Using the theory of $Spin ... More

On a uniform estimate for the quaternionic Calabi problemNov 02 2011Jul 27 2016We establish a C^0 a priori bound on the solutions of the quaternionic Calabi-Yau equation (of Monge-Ampere type) on compact HKT manifolds with a locally flat hypercomplex structure. As an intermediate step, we prove a quaternionic version of the Gauduchon ... More

Proof of the main conjecture on g-areasNov 06 2014In this paper, we prove the main conjecture on $g$-areas that was announced by the first author in 2004. It states that the $g$-area of any Hamiltonian diffeomorphism $\phi$ is equal to the positive Hofer distance between $\phi$ and the subspace of Hamiltonian ... More

Comment on Phys. Rev. B 83, 054515 (2011) by V. G. Kogan and J. Schmalian and comment on their reply Phys. Rev. B 86, 016502 (2012)May 18 2011Aug 24 2012The recent paper by V. G. Kogan and J. Schmalian Phys. Rev. B 83, 054515 (2011) argues that the widely used two-component Ginzburg-Landau (GL) models are not correct, and further concludes that in the regime which is described by a GL theory there could ... More

Microscopic theory of type-1.5 superconductivity in multiband systemsFeb 28 2011Sep 16 2011We report a self-consistent microscopic theory of characteristic length scales, vortex structure and type-1.5 superconducting state in two-band systems using two-band Eilenberger formalism.

Microscopic derivation of two-component Ginzburg-Landau model and conditions of its applicability in two-band systemsOct 07 2011Apr 04 2012We report a microscopic derivation of two-component Ginzburg-Landau (GL) field theory and the conditions of its validity in two-band superconductors. We also investigate the conditions when microscopically derived or phenomenological GL models fail and ... More

Topological defects in mixtures of superconducting condensates with different chargesMar 13 2014Jun 18 2014We investigate the topological defects in phenomenological models describing mixtures of charged condensates with commensurate electric charges. Such situations are expected to appear for example in liquid metallic deuterium. This is modeled by a multicomponent ... More

Second critical temperature in conventional superconductorsApr 24 2019We demonstrate that in a BCS superconductor, superconducting gap survives at surfaces at higher temperatures than uniform superconductivity in the bulk. We show that by revising the Caroli-De Gennes-Matricon theory of a superconductor-vacuum boundary. ... More

Type-1.5 superconductivity in two-band systemsJul 12 2010In the usual Ginzburg-Landau theory the critical value of the ratio of two fundamental length scales in the thery $\kappa_c=1/\sqrt{2}$ separates regimes of type-I and type-II superconductivity. The latter regime possess thermodynamically stable vortex ... More

Fractional smoothness of images of logarithmically concave measures under polynomialsApr 30 2016We show that a measure on the real line that is the image of a log-concave measure under a polynomial of degree $d$ possesses a density from the Nikol'skii--Besov class of fractional order $1/d$. This result is used to prove an estimate of the total variation ... More

A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet)Feb 08 2015Apr 20 2015We prove a $C^0$ a priori estimate on a solution of the quaternionic Calabi problem on an arbitrary compact connected HKT-manifold. This generalizes earlier works where this result was proven under certain extra assumptions on the manifold.

Vortex matter in $U(1)\times U(1)\times\mathbb{Z}_2$ phase-separated superconducting condensatesOct 11 2014Jan 04 2015We study the properties of vortex solutions and magnetic response of two-component $U(1)\times U(1)\times\mathbb{Z}_2$ superconductors, with phase separation driven by intercomponent density-density interaction. Such a theory can be viewed arising from ... More

Skyrmionic state and stable half-quantum vortices in chiral p-wave superconductorsJan 13 2012Aug 24 2012Observability of half-quantum vortices and skyrmions in p-wave superconductors is an outstanding open question. Under the most common conditions, fractional flux vortices are not thermodynamically stable in bulk samples. Here we show that in chiral p-wave ... More

Unusual mechanism of vortex viscosity generated by mixed normal modes in superconductors with broken time reversal symmetryJun 26 2013Dec 28 2013We show that under certain conditions multiband superconductors with broken time-reversal symmetry have a new vortex viscosity-generating mechanism which is different from that in conventional superconductors. It appears due to the existence of mixed ... More

Type-1.5 superconductivity in muliband and other multicomponent systemsJun 28 2012Jan 06 2013Usual superconductors are classified into two categories as follows: type-1 when the ratio of the magnetic field penetration length (\lambda) to coherence length (\xi) with Ginzburg-Landau parameter \kappa=\lambda/\xi <1/\sqrt{2} and type-2 when \kappa ... More

K-theoretic invariants of Hamiltonian fibrationsAug 27 2015Jan 18 2019We introduce new invariants of Hamiltonian fibrations with values in the suitably twisted K-theory of the base. Inspired by techniques of geometric quantization, our invariants arise from the family analytic index of a family of natural $Spin^c$-Dirac ... More

Not quite unreasonable effectiveness of machine learning algorithmsApr 07 2018State-of-the-art machine learning algorithms demonstrate close to absolute performance in selected challenges. We provide arguments that the reason can be in low variability of the samples and high effectiveness in learning typical patterns. Due to this ... More

Quotients of groups of birational transformations of cubic Del Pezzo fibrationsJul 10 2019We prove that the group of birational transformations of a Del Pezzo fibration of degree 3 over a curve is not simple, by giving a surjective group homomorphism to a free product of infinitely many groups of order 2. As a consequence we also obtain that ... More

Lattice Pseudospin Model for $ν=1$ Quantum Hall BilayersJan 19 2002Jul 01 2002We present a new theoretical approach to the study of $\nu=1$ quantum Hall bilayer that is based on a systematic mapping of the microscopic Hamiltonian to an anisotropic SU(4) spin model on a lattice. To study the properties of this model we generalize ... More

Thin topological insulator film in a perpendicular magnetic fieldMar 10 2011May 10 2011We report on a study of an ultrathin topological insulator film with hybridization between the top and bottom surfaces, placed in a quantizing perpendicular magnetic field. We calculate the full Landau level spectrum of the film as a function of the applied ... More

Spin and Charge Transport on the Surface of a Topological InsulatorMay 10 2010Aug 16 2010We derive diffusion equations, which describe spin-charge coupled transport on the helical metal surface of a three-dimensional topological insulator. The main feature of these equations is a large magnitude of the spin-charge coupling, which leads to ... More

$ν=2$ Bilayer Quantum Hall System in Tilted Magnetic FieldJan 22 2002Jul 01 2002We report on a theoretical study of $\nu=2$ bilayer quantum Hall systems with a magnetic field that has a component parallel to the layers. As in the $\nu=1$ case, interlayer phase coherence is closely coupled to electron correlations and the Aharonov-Bohm ... More

Fractional Quantum Hall Effect in Weyl SemimetalsJul 03 2019Weyl semimetal may be thought of as a gapless topological phase protected by the chiral anomaly, where the symmetries involved in the anomaly are the $U(1)$ charge conservation and the crystal translational symmetry. The absence of a band gap in a weakly-interacting ... More