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Quasiparticle Interference and Symmetry of Superconducting Order Parameter in Strongly Electron-Doped Iron-based SuperconductorsMar 14 2019Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a sign-changing order-parameter in the Li$_{1-x}$Fe$_x$(OHFe)$_{1-y}$Zn$_y$Se superconductor with only electron pockets present, we study the possible Cooper-pairing ... More

Impurity resonance states in noncentrosymmetric superconductor $CePt_{3}Si$: a probe for Cooper-pairing symmetryMar 31 2008Jul 23 2008Motivated by the recent discovery of noncentrosymmetric superconductors, such as $CePt_{3}Si$, $CeRhSi_{3}$ and $CeIrSi_{3}$, we investigate theoretically the impurity resonance states with coexisting $s$- and p-wave pairing symmetries. Due to the nodal ... More

Reply to 'Difficulty in the Fermi-Liquid-Based Theory for the In-Plane Magnetic Anisotropy in Untwinned High-$T_c$ Superconductors'Oct 02 2007A Reply to the Comment by Hou-Jun Zhao and Jun Li

Temperature dependence of the nodal Fermi velocity in layered cupratesJul 26 2008We explain recently observed linear temperature dependence of the nodal Fermi velocity $v_F (T)$ in near-optimally doped cuprates. We argue that it originates from electron-electron interaction, and is a fundamental property of an arbitrary 2D Fermi liquid. ... More

Thermal screening at finite chemical potential on a topological surface and its interplay with proximity-induced ferromagnetismSep 13 2013Jul 15 2014Motivated by recent experiments on EuS/Bi$_2$Se$_3$ heterostructures, we study the temperature dependent screening effects on the surface of a three-dimensional topological insulator proximate to a ferromagnetically ordered system. In general, we find ... More

Strong-coupling topological Josephson effect in quantum wiresFeb 15 2011Apr 13 2012We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling, the exact solution reproduces the perturbative result for the energy containing ... More

Dichotomy between in-plane magnetic susceptibility and resistivity anisotropies in extremely strained $BaFe_{2}As_{2}$Oct 18 2016The in-plane resistivity and uniform magnetic susceptibility anisotropies of $BaFe_{2}As_{2}$ are obtained with a new method, in which a large symmetry-breaking uniaxial strain is applied using a substrate with a very anisotropic thermal expansion. The ... More

Magnetic degeneracy and hidden metallicity of the spin density wave state in ferropnictidesNov 09 2009Dec 01 2009We analyze spin density wave (SDW) order in iron-based superconductors and electronic structure in the SDW phase. We consider an itinerant model for Fe-pnictides with two hole bands centered at $(0,0)$ and two electron bands centered at $(0,\pi)$ and ... More

Fluctuation-induced magnetization dynamics and criticality at the interface of a topological insulator with a magnetically ordered layerJul 11 2012Dec 04 2012We consider a theory for a two-dimensional interacting conduction electron system with strong spin-orbit coupling on the interface between a topological insulator and the magnetic (ferromagnetic or antiferromagnetic) layer. For the ferromagnetic case ... More

Semi-metal-insulator transition on the surface of a topological insulator with in-plane magnetizationApr 10 2013Aug 29 2013A thin film of ferromagnetically ordered material proximate to the surface of a three-dimensional topological insulator explicitly breaks the time-reversal symmetry of the surface states. For an out-of-plane ferromagnetic order parameter on the surface, ... More

Quasiparticle interference in heavy Fermion superconductor CeCoIn_5Aug 23 2011We investigate the quasiparticle interference in the heavy Fermion superconductor CeCoIn_5 as direct method to confirm the d-wave gap symmetry. The ambiguity between d_{xy} and d_{x^2-y^2} symmetry remaining from earlier specific heat and thermal transport ... More

Superconductivity in $β$-pyrochlore superconductor KOs$_{2}$O$_{6}$: treatment within strong-coupling Eliashberg theoryMar 17 2008Sep 26 2008We study the influence of the rattling phonons on superconductivity in $\beta$-pyrochlore KOs$_{2}$O$_{6}$ compound based on the strong-coupling Eliashberg approach. In particular, analyzing the specific heat data we find that the rattling phonon frequency ... More

Magnetic impurity resonance states and symmetry of the superconducting order parameter in iron-based superconductorsNov 19 2009Dec 16 2009We investigate the effect of magnetic impurities on the local quasiparticle density of states (LDOS) in iron-based superconductors. Employing the two-orbital model where 3$d$ electron and hole conduction bands are hybridizing with the localized $f$-orbital ... More

Evolution of the multiband RKKY interaction: Application to iron pnictides and chalcogenidesJan 28 2013The indirect RKKY interaction in iron pnictide and chalcogenide metals is calculated for a simplified four bands Fermi surface (FS) model. We investigate the specific multi-band features and show that distinct length scales of the RKKY oscillations appear. ... More

Model of Nonadiabatic to Adiabatic Dynamical Quantum Phase Transition in Photoexcited SystemsJul 25 2014Sep 20 2014We study the ultrafast dynamic process in photoexcited systems and find that the Franck-Condon or Landau-Zener tunneling between the photoexcited state and the ground state is abruptly blocked with increasing the state coupling from nonadiabatic to adiabatic ... More

Signatures of non-monotonic d-wave gap in electron-doped cupratesSep 26 2007We address the issue whether the data on optical conductivity and Raman scattering in electron-doped cuprates below $T_c$ support the idea that the $d-$wave gap in these materials is non-monotonic along the Fermi surface. We calculate the conductivity ... More

Higgs Mechanism, Phase Transitions, and Anomalous Hall Effect in Three-Dimensional Topological SuperconductorsApr 29 2015Nov 17 2015We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axion-like magnetoelectric ... More

Polar Kerr effect from a time-reversal symmetry breaking unidirectional charge density waveJan 02 2015We analyze the Hall conductivity $\sigma_{xy}(\omega)$ of a charge ordered state with momentum $\mathbf{Q}=(0,2Q)$ and calculate the intrinsic contribution to the Kerr angle $\Theta_K$ using the fully reconstructed tight-binding band structure for layered ... More

RKKY interaction in SDW phase of iron-based superconductorsSep 21 2011Using the multiband model we analyze the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the magnetic impurities in layered ferropnictide superconductors. In the normal state the interaction is spin isotropic and is dominated by the nesting features ... More

Investigation of magnetic phases in parent compounds of Iron-chalcogenides via quasiparticle scattering interferenceMay 06 2016We employ a five-orbital tight-binding model to develop the mean field solution for various possible spin density wave states in the iron-chalcogenides. The quasiparticle interference (QPI) technique is applied to detect signatures of these states due ... More

Superconductivity vs bound state formation in a two-band superconductor with small Fermi energy -- applications to Fe-pnictides/chalcogenides and doped SrTiO3Jan 07 2016We analyze the interplay between superconductivity and the formation of bound pairs of fermions (BCS-BEC crossover) in 2D models of interacting fermions with small Fermi energy EF and weak attractive interaction, which extends to energies well above EF. ... More

Collective magnetic excitations of $C_{4}$ symmetric magnetic states in iron-based superconductorsAug 11 2016We study the collective magnetic excitations of the recently discovered $C_{4}$ symmetric spin-density wave states of iron-based superconductors with particular emphasis on their orbital character based on an itinerant multiorbital approach. This is important ... More

Interaction of Skyrmions and Pearl Vortices in Superconductor-Chiral Ferromagnet HeterostructuresOct 23 2018Mar 01 2019We investigate a hybrid heterostructure with magnetic skyrmions (Sk) inside a chiral ferromagnet interfaced by a thin superconducting film via an insulating barrier. The barrier prevents the electronic transport between the superconductor and the chiral ... More

Bound state of 4$f$-excitation and magnetic resonance in unconventional superconductorsFeb 26 2009We analyze the influence of unconventional superconductivity on crystalline electric field (CEF) excitations of rare earth ions in novel superconductors. We show that resonant magnetic excitations of the conduction electrons that have been observed in ... More

Electronic properties, low-energy Hamiltonian and superconducting instabilities in CaKFe$_4$As$_4$Jun 27 2017We analyze the electronic properties of the recently discovered stoichiometric superconductor CaKFe$_4$As$_4$ by combining an ab initio approach and a projection of the band structure to a lowenergy tight-binding Hamiltonian, based on the maximally localized ... More

Short-time dynamics in $s+is$-wave superconductor with incipient bandsApr 16 2018Motivated by the recent observation of the time-reversal symmetry broken state in K-doped BaFe$_2$As$_2$ superconducting alloys, we theoretically study the collective modes and the short time dynamics of the superconducting state with $s+is$-wave order ... More

s+is superconductivity with incipient bands: doping dependence and STM signaturesApr 26 2017Jul 26 2017Motivated by the recent observations of small Fermi energies and comparatively large superconducting gaps, present also on bands not crossing the Fermi energy (incipient bands) in iron-based superconductors, we analyse the doping evolution of superconductivity ... More

Eliashberg theory of superconductivity and inelastic rare-earth impurity scattering in filled skutterudite La$_{1-x}$Pr$_{x}$Os$_{4}$Sb$_{12}$Sep 24 2007Jan 02 2008We study the influence of inelastic rare-earth impurity scattering on electron-phonon mediated superconductivity and mass renormalization in (La$_{1-x}$Pr$_{x}$)Os$_{4}$Sb$_{12}$ compounds. Solving the strong coupling Eliashberg equations we find that ... More

The resonance peak in the electron-doped cuprate superconductorsFeb 15 2007Nov 22 2007We study the emergence of a magnetic resonance in the superconducting state of the electron-doped cuprate superconductors. We show that the recently observed resonance peak in the electron-doped superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ ... More

Theory of Raman response in a superconductor with extended s-wave symmetry: Application to Fe-pnictidesJan 14 2009Feb 24 2009We argue that Raman study of Fe-pnictides is a way to unambiguously distinguish between various superconducting gaps proposed for these materials. We show that $A_{1g}$ Raman intensity has a true resonance peak below $2\Delta$ for extended s-wave superconducting ... More

Spin susceptibility in bilayered cuprates: resonant magnetic excitationsNov 09 2006We study the momentum and frequency dependence of the dynamical spin susceptibility in the superconducting state of bilayer cuprate superconductors. We show that there exists a resonance mode in the odd as well as the even channel of the spin susceptibility, ... More

Spin and Charge Josephson effects between non-uniform superconductors with coexisting helimagnetic orderOct 11 2005Feb 16 2006We consider the spin and charge Josephson current between two non-uniform Fulde-Ferrel-Larkin-Ovchinnikov superconductors with helimagnetic order. We demonstrate that the presence of the helimagnetic phase generates a spin Josephson effect and leads to ... More

Theory of nonequilibrium dynamics of multiband superconductorsMay 22 2012Jan 09 2013We study the nonequilibrium dynamics of multiband BCS superconductors subjected to ultrashort pump pulses. Using density-matrix theory, the time evolution of the Bogoliubov quasiparticle densities and the superconducting order parameters are computed ... More

Surface state tunneling signatures in two-component superconductor UPt$_3$Aug 29 2016Quasiparticle interference (QPI) imaging of Bogoliubov excitations in quasi-two dimensional unconventional superconductors has become a powerful technique for measuring the superconducting gap and its symmetry. Here, we present the extension of this method ... More

Holomorphic Effective Action of N=2 SYM Theory from Harmonic Superspace with Central ChargesAug 08 1999Sep 15 1999We compute the one-loop holomorphic effective action of the massless Cartan sector of N=2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal components of the gauge superfield. ... More

Interaction of Skyrmions and Pearl Vortices in Superconductor-Chiral Ferromagnet HeterostructuresOct 23 2018We investigate a hybrid heterostructure with magnetic skyrmions (Sk) inside a chiral ferromagnet interfaced by a thin superconducting film via an insulating barrier. The barrier prevents the electronic transport between the superconductor and the chiral ... More

Strong Competition of Superconducting and Magnetic Order Parameters in Ba1-xNaxFe2As2Oct 25 2012We study the interplay of magnetic and superconducting order in single crystalline hole doped Ba1-xNaxFe2As2 using muon spin relaxation. We find microscopic coexistence of magnetic order and superconductivity. In a strongly underdoped specimen the two ... More

Anisotropic spin fluctuations in Sr$_2$RuO$_4$: role of spin-orbit coupling and induced strainAug 24 2016We analyze the spin anisotropy of the magnetic susceptibility of Sr$_2$RuO$4$ in presence of spin-orbit coupling and anisotropic strain using quasi-two-dimensional tight-binding parametrization fitted to the ARPES results. Similar to the previous observations ... More

Multiband Superconductivity in Spin Density Wave MetalsJul 07 2009We study the emergence of multiband superconductivity with $s$- and $d-$wave symmetry on the background of spin density wave (SDW). We show that the SDW coherence factors renormalize the momentum dependence of the superconducting (SC) gap, yielding a ... More

Spin-orbit coupling, minimal model and potential Cooper-pairing from repulsion in BiS$_2$-superconductorsNov 15 2017We develop the realistic minimal electronic model for recently discovered BiS$_2$ superconductors including the spin-orbit coupling based on a first-principles band structure calculations. Due to strong spin-orbit coupling, characteristic for the Bi-based ... More

Tricolor Technique for Visualization of Spatial Variations of Polydisperse Dust in Gas-Dust FlowsMar 27 2018The aim of this work is to construct an algorithm for visualizing a polydisperse phase of solid particles (dust) in an inhomogeneous flow of a two-phase gas-dust mixture that would allow us to see, within one plot, the degree of polydispersity of the ... More

Antiferromagnetism in Iron-Based Superconductors: Selection of Magnetic Order and Quasiparticle InterferenceFeb 28 2014The recent discovery of superconductivity in the iron-based layered pnictides with T_c ranging between 26 and 56K generated enormous interest in the physics of these materials. Here, we review some of the peculiarities of the antiferromagnetic order in ... More

Scanning tunneling spectroscopy as a probe of multi-Q magnetic states of itinerant magnetsJul 16 2016The combination of electronic correlations and Fermi surfaces with multiple nesting vectors can lead to the appearance of complex multi-Q magnetic ground states, hosting unusual states such as chiral density-waves and quantum Hall insulators. Distinguishing ... More

Novel neutron resonance mode in $d_{x^2-y^2}$ superconductorsSep 22 2004We show that a new resonant magnetic excitation at incommensurate momenta, observed recently by inelastic neutron scattering experiments on YBa$_2$Cu$_3$O$_{6.85}$ and YBa$_2$Cu$_3$O$_{6.6}$, is a {\it spin exciton}. Its location in the magnetic Brillouin ... More

Structural and Magnetic Characterization of Ni2MnBO5 ludwigiteSep 29 2015Single crystals of ludwigite Ni2MnBO5 were synthesized by flux growth technique. The detailed structural and magnetic characterizations of the synthesized samples have been carried out. The cations composition of the studied crystal was determined using ... More

Spin excitations and the Fermi surface of superconducting FeSFeb 09 2017High-temperature superconductivity occurs near antiferromagnetic instabilities and nematic state. Debate remains on the origin of nematic order in FeSe and its relation with superconductivity. Here, we use transport, neutron scatter- ing and Fermi surface ... More

Curves of infinite genus I Riemann--Roch theorem for small degreeFeb 07 2002The most useful and interesting line bundles over algebraic curves of a very high genus have the ratio \delta of the degree to the genus close to half-integer values, usually \delta \approx 0, \delta \approx 1/2, or \delta \approx 1; the numeric properties ... More

Geometic vertex operatorsMay 21 1998Sep 27 2002Vertex operators, being families of birational transformations of infinite-dimensional algebraic ``varieties'' M, act on appropriate line bundles on M. However, they act on (meromorphic) sections only as_partial operators_: they are defined on a subspace ... More

Error Bound for Compound Wishart MatricesFeb 23 2014Mar 12 2014In this paper we consider non-asymptotic behavior of the real compound Wishart matrices that generalize the classical real Wishart distribution. In particular, we consider matrices of the form 1/nXBX', where X consists of real centered Gaussian elements ... More

An example of a reducible Severi varietyNov 24 2013Dec 25 2013We construct a positive-dimensional, reducible Severi variety on a toric surface.

On Severi varieties on Hirzebruch surfacesJul 31 2006In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.

Detecting quasiconvexity: algorithmic aspectsJun 27 1995The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$. This provides ... More

Limiting distribution of visits of sereval rotations to shrinking intervalsMay 10 2010We show that given $n$ normalized intervals on the unit circle, the numbers of visits of $d$ random rotations to these intervals have a joint limiting distribution as lengths of trajectories tend to infinity. If $d$ then tends to infinity, then the numbers ... More

A Generalization of a Result of Hardy and LittlewoodSep 18 2007Nov 08 2011In this note we study the growth of \sum_{m=1}^M\frac1{\|m\alpha\|} as a function of M for different classes of \alpha\in[0,1). Hardy and Littlewood showed that for numbers of bounded type, the sum is \simeq M\log M. We give a very simple proof for it. ... More

Common information revisitedApr 16 2011Jun 18 2012One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$ and $y$ measures ... More

Fano threefolds with canonical Gorenstein singularities and big degreeAug 12 2009Nov 19 2014We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.

One base point free theorem for weak log Fano threefoldsJun 02 2009Feb 01 2010Let $(X,D)$ be log canonical pair such $\dim X = 3$ and the divisor $-(K_X + D)$ is nef and big. For a special class of such $(X,D)$'s we prove that the linear system $|-n(K_{X}+D)|$ is free for $n \gg 0$.

The Phase-Space Noncommutativity Effect on the Large and Small Wavefunction Components Approach at Dirac EquationAug 03 2014Sep 16 2018By the large and small wave-function components approach we achieved the nonrela-tivistic limit of the Dirac equation in interaction with an electromagnetic potential in noncommutative phase-space, and we tested the effect of the phase-space noncommutativity ... More

Sequences modulo one: convergence of local statisticsOct 16 2014We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in $\mathbb R^2$ and on the sequence $\sqrt n\bmod1 $.

On Severi varieties and Moduli spaces of curves in arbitrary characteristicSep 06 2004Apr 26 2006This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

Some invariance properties of cyclic cohomology with coefficientsNov 04 2016In this paper, we further explore the conceptual approach to cyclic cohomology with coefficients. In particular we give a derived version of the definition with better invariance properties. We show that the new definition agrees with the old under certain ... More

Enumeration of rational curves with cross-ratio constraintsSep 24 2015Oct 21 2016In this paper we prove the algebraic-tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus and in the boundary divisor, the map has prescribed ... More

Convex and star-shaped sets associated with stable distributionsJul 02 2007Mar 22 2008It is known that each symmetric stable distribution in $R^d$ is related to a norm on $R^d$ that makes $R^d$ embeddable in $L_p([0,1])$. In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to a convex set ... More

Musings on generic-case complexityMay 13 2015We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.

Binding energy of a Cooper pairs with non-zero center of mass momentum in d-wave superconductorsJan 23 2007The binding energy of Cooper pairs has been calculated for the case of d-wave symmetry of the superconducting gap in layered cuprate superconductors. We assume that Cooper pairs are formed by the short range potential and then derive the binding energy ... More

The q-Deformed Harmonic Oscillator, Coherent States, and the Uncertainty RelationOct 10 2008For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We calculate the product ... More

A simplified spectrometer based on a fast digital oscilloscope for the measurement of high energy $γ$-raysMay 28 2014A simplified digital spectrometer for the study of $\gamma$-rays with energies up to $\sim100$ MeV is presented and tested. The spectrometer is only consisted of a fast digital oscilloscope and three scintillation detectors which can work in single or ... More

Random length-spectrum rigidity for free groupsJan 12 2010Feb 04 2011We say that a subset $S\subseteq F_N$ is \emph{spectrally rigid} if whenever $T_1, T_2\in cv_N$ are points of the (unprojectivized) Outer space such that $||g||_{T_1}=||g||_{T_2}$ for every $g\in S$ then $T_1=T_2$ in $\cvn$. It is well-known that $F_N$ ... More

A non-quasiconvexity embedding theorem for hyperbolic groupsApr 11 1997We show that if $G$ is a non-elementary torsion-free word hyperbolic group then there exists another word hyperbolic group $G^*$, such that $G$ is a subgroup of $G^*$ but $G$ is not quasiconvex in $G^*$.

Quasiconvexity and AmalgamsJun 27 1995We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that is such that ... More

An integral weight realization theorem for subset currents on free groupsNov 26 2012Jul 18 2016We prove that if $N\ge 2$ and $\alpha: F_N\to \pi_1(\Gamma)$ is a marking on $F_N$, then for any integer $r\ge 2$ and any $F_N$-invariant collection of non-negative integral "weights" associated to all subtrees $K$ of $\widetilde \Gamma$ of radius $\le ... More

Clusters, currents and Whitehead's algorithmNov 19 2005Sep 12 2006Using geodesic currents, we provide a theoretical justification for some of the experimental results regarding the behavior of Whitehead's algorithm on non-minimal inputs, that were obtained by Haralick, Miasnikov and Myasnikov via pattern recognition ... More

Fokker-Planck formalism in magnetic resonance simulationsMay 15 2016May 26 2016This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly ... More

On transport properties of isotropic quasiperiodic $XY$ spin chainsMay 26 2015We consider isotropic $XY$ spin chains whose magnetic potentials are quasiperiodic and the effective one-particle Hamiltonians have absolutely continuous spectra. For a wide class of such $XY$ spin chains, we obtain lower bounds on their Lieb--Robinson ... More

On the quotient of $\mathbb{C}^4$ by a finite primitive group of type (I)Feb 08 2012Sep 29 2012We study rationality problem for the quotient of $\mathbb{C}^4$ by a finite primitive group $G$ of Type (I). We prove that this quotient is a rational variety for any such $G$.

Remark on polarized K3 surfaces of genus 36Apr 25 2010Dec 16 2010Smooth primitively polarized $\mathrm{K3}$ surfaces of genus 36 are studied. It is proved that all such surfaces $S$, for which there exists an embedding $\mathrm{R} \hookrightarrow \mathrm{Pic}(S)$ of some special lattice $\mathrm{R}$ of rank 2, are ... More

Invariant-equivariant representation learning for multi-class dataFeb 08 2019Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: ... More

Thompson's conjecture for alternating groupNov 17 2016Let $G$ be a finite group, and let $N(G)$ be the set of sizes of its conjugacy classes. We show that if a finite group $G$ has trivial center and $N(G)$ equals to $N(Alt_n)$ or $N(Sym_n)$ for $n\geq 23$, then $G$ has a composition factor isomorphic to ... More

The frequency space of a free groupNov 05 2003Aug 27 2004We analyze the structure of the \emph{frequency space} $Q(F)$ of a nonabelian free group $F=F(a_1,...,a_k)$ consisting of all shift-invariant Borel probability measures on $\partial F$ and construct a natural action of $Out(F)$ on $Q(F)$. In particular ... More

Large Deviations and Effective EquidistributionNov 11 2015We study large deviations for measurable averaging operators on state spaces of dynamical systems. Our main motivation is the Hecke operators on the modular curve Y_0(p^n) and their generalization to higher rank S-arithmetic quotients. We prove a relatively ... More

First exit times of solutions of stochastic differential equations driven by multiplicative Levy noise with heavy tailsMay 28 2012In this paper we study first exit times from a bounded domain of a gradient dynamical system $\dot Y_t=-\nabla U(Y_t)$ perturbed by a small multiplicative L\'evy noise with heavy tails. A special attention is paid to the way the multiplicative noise is ... More

Network patterns and strength of orbital currents in layered cupratesNov 28 2001In a frame of the $t-J-G$ model we derive the microscopical expression for the circulating orbital currents in layered cuprates using the anomalous correlation functions. In agreement with $\mu$-on spin relaxation ($\mu$SR), nuclear quadrupolar resonance ... More

Currents on free groupsDec 07 2004Sep 19 2005We study the properties of geodesic currents on free groups, particularly the "intersection form" that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces.

An example of a non-quasiconvex subgroup of a word hyperbolic group with exotic limit setJun 29 1995We construct an example of a torsion free freely indecomposable finitely presented non-quasiconvex subgroup $H$ of a word hyperbolic group $G$ such that the limit set of $H$ is not the limit set of a quasiconvex subgroup of $G$. In particular, this gives ... More

On AdS_4 x CP^3 T-dualityNov 03 2010Nov 09 2010We give a supergravity treatment of the set of bosonic and fermionic T-dualities in the AdS_4 x CP^3 background. We consider T-dualities along three flat AdS_4 directions, three complexified isometries of CP^3, and six fermionic T-dualities. Concentrating ... More

Triple Higgs coupling in the most general 2HDM at SM-like scenarioOct 28 2015Oct 12 2016We consider the triple Higgs coupling for $h(125)$ Higgs boson within the most general 2HDM. At moderate values of parameters of model, allowing by modern data, noticeable deviation of this coupling from its SM value is improbable. This deviation can ... More

Information theory and adaptationNov 24 2010In this Chapter, we ask questions (1) What is the right way to measure the quality of information processing in a biological system? and (2) What can real-life organisms do in order to improve their performance in information-processing tasks? We then ... More

Nonlinear wave equation, nonlinear Riemann problem, and the twistor transform of Veronese websJun 04 2000Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave ... More

Effective equidistribution of horocycle liftsJul 16 2016We give a rate of equidistribution of lifts of horocycles from the space $\mathrm{SL}(2,\mathbb Z)\backslash \mathrm{SL}(2, \mathbb R)$ to the space $\mathrm{ASL}(2,\mathbb Z)\backslash \mathrm{ASL}(2,\mathbb R)$, making effective a theorem of Elkies ... More

Modal logics of finite direct powers of $ω$ have the finite model propertyMar 11 2019Let $(\omega^n,\preceq)$ be the direct power of $n$ instances of $(\omega,\leq)$, natural numbers with the standard ordering, $(\omega^n,\prec)$ the direct power of $n$ instances of $(\omega,<)$. We show that for all finite $n$, the modal logics of $(\omega^n,\preceq)$ ... More

Generic-case complexity of Whitehead's algorithm, revisitedMar 17 2019In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$ are "strictly ... More

Charged Compact Stars in $f(\mathcal{G})$ GravitySep 15 2018This work is devoted to investigate some of the interior configuration of static anisotropic spherical stellar charged structures in the regime of $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the Gauss Bonnet invariant. The structure of particular ... More

On some integral transforms of Coulomb functions related to three-dimensional proper Lorentz groupApr 07 2019Considering the relationship between two bases in representation space of the three-dimensional proper Lorentz group, we derive some formulas with integrals involving Coulomb wave functions, which can be considered as Fourier, Mellin, $K$-Bessel, Hankel ... More

Expansions for solutions of the Schlesinger equation at a singular pointDec 10 2012A local behavior of solutions of the Schlesinger equation is studied. We obtain expansions for this solutions, which converge in some neighborhood of a singular point. As a corollary the similar result for the sixth Painlev\'e equation was obtained. In ... More

Upper semi-continuity of the Hilbert-Kunz multiplicityJul 24 2014We prove that the Hilbert-Kunz multiplicity is upper semi-continuous in F-finite rings and algebras of essentially finite type over an excellent local ring.

Joint Equidistribution of CM PointsOct 12 2017Oct 22 2018We prove the mixing conjecture of Michel and Venkatesh for toral packets with negative fundamental discriminants and split at two fixed primes; assuming all splitting fields have no exceptional Landau-Siegel zero. As a consequence we establish for arbitrary ... More

The geometry of relative Cayley graphs for subgroups of hyperbolic groupsJan 07 2002Jan 09 2002We show that if H is a quasiconvex subgroup of a hyperbolic group G then the relative Cayley graph Y (also known as the Schreier coset graph) for G/H is Gromov-hyperbolic. We also observe that in this situation if G is torsion-free and non-elementary ... More

Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. BellSep 13 2016May 02 2017In \cite{Ka14} we produced an algorithm for deciding whether or not an element $\phi\in Out(F_N)$ is an iwip ("fully irreducible") automorphism. At several points that algorithm was rather inefficient as it involved some general enumeration procedures ... More

On purely loxodromic actionsApr 20 2015Jul 07 2015We construct an example of an isometric action of $F(a,b)$ on a $\delta$-hyperbolic graph $Y$, such that this action is acylindrical, purely loxodromic, has asymptotic translation lengths of nontrivial elements of $F(a,b)$ separated away from $0$, has ... More

Generic-case complexity of Whitehead's algorithm, revisitedMar 17 2019Mar 21 2019In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$ are "strictly ... More