Results for "Dmitry K. Efimkin"
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Moving solitons in a one-dimensional fermionic superfluidAug 27 2014Feb 18 2015A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton ... More Spin-plasmons in topological insulatorJul 23 2011Collective plasmon excitations in a helical electron liquid on the surface of strong three-dimensional topological insulator are considered. The properties and internal structure of these excitations are studied. Due to spin-momentum locking in helical ... More Non-Markovian quantum friction of bright solitons in superfluidsDec 23 2015May 04 2016We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov ... More Amperean Pairing at the Surface of Topological InsulatorsMar 13 2016Aug 12 2016The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards ... More Essential spectrum of a limit of self--adjoint operatorsAug 23 2012Aug 27 2012For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence. Zero Energy Bound States in Many--Particle SystemsDec 01 2011It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed ... More Integrals of open 2D latticesDec 21 2009We present an explicit formula for integrals of the open 2D Toda lattice of type $A_n$. This formula is applicable for various reductions of this lattice. To illustrate the concept we find integrals of the Toda $G_2$ lattice. We also reveal a connection ... More Universal low-energy behavior in three-body systemsJan 24 2014Mar 03 2015We consider a pairwise interacting quantum 3-body system in 3-dimensional space with finite masses and the interaction term $V_{12} + \lambda(V_{13} + V_{23})$, where all pair potentials are assumed to be nonpositive. The pair interaction of the particles ... More Charged skyrmions on the surface of a topological insulatorDec 02 2014Feb 13 2015We consider the interplay between magnetic skyrmions in an insulating thin film and the Dirac surface states of a 3D topological insulator (TI), coupled by proximity effect. The magnetic texture of skyrmions can lead to confinement of Dirac states at ... More Zero Energy Bound States in Three--Particle SystemsDec 02 2009Jan 22 2010Under certain restrictions on pair--potentials it is proved that the eigenvalues in the three--particle system are absorbed at zero energy threshold if there is no negative energy bound states and zero energy resonances in particle pairs. On non-Abelian Toda $A_2^{(1)}$ model and related hierarchiesDec 21 2009We study limiting cases of the two known integrable chiral-type models with tree-dimensional configuration space. One of the initial models is the non-Abelian Toda $A_2^{(1)}$ model and the other was found by means of the symmetry approach by A.G. Meshkov ... More Selecting fast folding proteins by their rate of convergenceApr 02 2012Feb 06 2013We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using only the very ... More Lagrangian Relaxation for MAP Estimation in Graphical ModelsSep 28 2007We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph, but subject ... More A microprocessor based on a two-dimensional semiconductorDec 03 2016The advent of microcomputers in the 1970s has dramatically changed our society. Since then, microprocessors have been made almost exclusively from silicon, but the ever-increasing demand for higher integration density and speed, lower power consumption ... More On Small Gaps in the Length SpectrumFeb 15 2016We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps. On the ... More Catalog of Nearby Galaxies and the Local Cosmic WebOct 04 2004We compiled an all-sky catalog of 451 nearby galaxies, each having an individual distance estimate $D \la 10$ Mpc or the radial velocity $V_{LG} < 550$ km s$^{-1}$. The catalog contains data on basic optical and HI properties of the galaxies: their diameters, ... More Topological Semantics and DecidabilityMar 05 2007Jun 01 2007It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of $T_0$, ... More On the derivative of two functions from Denjoy-Tichy-Uitz familyFeb 14 2013Dec 01 2013The family of functions, we investigate in this article, was originally introduced by A.Denjoy and later rediscovered by R Tichy and J. Uitz. We denote the functions of the family by $g_{\lambda}(x),$ where $\lambda\in(0,1)$. The definition will be given ... More Asymptotic dimension of one relator groupsJul 21 2006We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov and give an estimate of their asymptotic dimension in terms of the relator length. Clown: a Microprocessor Simulator for Operating System StudiesJul 21 2012In this paper, I present the design and implementation of Clown--a simulator of a microprocessor-based computer system specifically optimized for teaching operating system courses at undergraduate or graduate levels. The package includes the simulator ... More Error bounds for approximations with deep ReLU networksOct 03 2016We study how approximation errors of neural networks with ReLU activation functions depend on the depth of the network. We establish rigorous error bounds showing that deep ReLU networks are significantly more expressive than shallow ones as long as approximations ... More Commuting symplectomorphisms and Dehn twists in divisorsMay 18 2014Jun 02 2016Two commuting symplectomorphisms of a symplectic manifold give rise to actions on Floer cohomologies of each other. We prove the elliptic relation saying that the supertraces of these two actions are equal. In the case when a symplectomorphism $f$ commutes ... More Storage option an Analytic approachNov 04 2010May 28 2012The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show ... More On extension for infinite horizon game of pursuit-evasionDec 16 2010The extension of a conflict control problem with infinite horizon is constructed. This extension is the projective limit of restricted games. Relations between "sensitivity to target set" and the existence of the optimal control are studied. Special attention ... More Classical Interaction Cannot Replace Quantum NonlocalityJan 08 2009We present a two-player communication task that can be solved by a protocol of polylogarithmic cost in the simultaneous message passing model with classical communication and shared entanglement, but requires exponentially more communication in the classical ... More Classical Interaction Cannot Replace a Quantum MessageMar 23 2007Feb 21 2008We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model. Enstrophy growth in the viscous Burgers equationFeb 09 2012We study bounds on the enstrophy growth for solutions of the viscous Burgers equation on the unit circle. Using the variational formulation of Lu and Doering, we prove that the maximizer of the enstrophy's rate of change is sharp in the limit of large ... More Courant-Dorfman algebras and their cohomologyFeb 27 2009Nov 30 2009We introduce a new type of algebra, the Courant-Dorfman algebra. These are to Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson algebras to Poisson manifolds. We work with arbitrary rings and modules, without any regularity, ... More The Frequency of Rapid Rotation Among K Giant StarsMar 07 2011We present the results of a search for unusually rapidly rotating giant stars in a large sample of K giants (~1300 stars) that had been spectroscopically monitored as potential targets for the Space Interferometry Mission's Astrometric Grid. The stars ... More Microlocal CategoryNov 29 2015Given a compact symplectic manifold whose symplectic form has integer periods, one associates to it a dg category based on the microlocal analysis according to Kashiwara-Schapira Medical Process Modeling: an Artifact-Centric ApproachMar 19 2013In this position paper we argue that just as traditional business process modeling has been adopted to deal with clinical pathways, also the artifact-centric process modeling technique may be successfully used to model various kinds of medical processes: ... More Moment inversion problem for piecewise D-finite functionsJan 29 2009Jul 01 2009We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial ... More The Parisi formula for mixed $p$-spin modelsDec 19 2011Mar 31 2014The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for ... More Spin glass models from the point of view of spin distributionsMay 16 2010May 24 2013In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can think of this ... More The Baum-Connes conjecture for countable subgroups of SL(2)Dec 21 2007We present an alternative approach to the result of Guentner, Higson, and Weinberger concerning the Baum-Connes conjecture for finitely generated subgroups of SL(2,C). Using finite-dimensional methods, we show that the Baum-Connes assembly map for such ... More Multiplicity One Theorems and Invariant DistributionsJul 06 2009This is my PhD thesis submitted to the Weizmann Institute of Science. It is based on the papers [AG08c], [AG08d], [AGRS07], [AGS08], [AGS09], [Aiz08] and [SZ08]. This thesis includes an introduction to Gelfand pairs and invariant distributions, a list ... More Cavity method in the spherical Sherrington-Kirkpatrick modelApr 04 2006Aug 18 2007We develop a cavity method in the spherical Sherrington-Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization. Large regular QCD coupling at Low Energy?Jul 09 2008The issue is the expediency of the QCD notions use in the low energy region down to the confinement scale, and, in particular, the efficacy of the QCD invariant coupling \bar{\alpha}_s(Q^2) with a minimal analytic modification in this domain. To this ... More Gromov's macroscopic dimension conjectureApr 30 2009In this note we construct a closed 4-manifold having torsion-free fundamental group and whose universal covering is of macroscopic dimension 3. This yields a counterexample to Gromov's conjecture about the falling of macroscopic dimension. Residue Formulation of Chern Character on Smooth ManifoldsMay 07 2005The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown by Quillen ... More Some applications of homogeneous dynamics to number theoryOct 18 2002This survey paper is not a complete reference guide to number-theoretical applications of ergodic theory. Instead, it considers an approach to a class of problems involving Diophantine properties of $n$-tuples of real numbers, namely, describes a specific ... More Chaos in temperature in generic 2p-spin modelsFeb 12 2015Dec 18 2015We prove chaos in temperature for even $p$-spin models which include sufficiently many $p$-spin interaction terms. Our approach is based on a new invariance property for coupled asymptotic Gibbs measures, similar in spirit to the invariance property that ... More Quasi-Lie bialgebroids and twisted Poisson manifoldsDec 17 2001Nov 21 2002We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context of string theory, ... More On a criterion of properness of multimapsNov 09 2009The close relation between properness and closedness of maps is well-known. For instance, for Fredholm mappings of infinite dimensional Banach manifolds, these properties are equivalent. On the other hand, properness of maps plays an important role for ... More Quantum Money with Classical VerificationSep 02 2011Mar 15 2012We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. ... More Improved bounds for arithmetic progressions in product setsFeb 12 2015Let $B$ be a set of natural numbers of size $n$. We prove that the length of the longest arithmetic progression contained in the product set $B.B = \{bb'| \, b, b' \in B\}$ cannot be greater than $O(n \log n)$ which matches the lower bound provided in ... More Translationally invariant nonlinear Schrodinger latticesMar 10 2006Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. ... More Free energy in the Potts spin glassDec 01 2015Dec 28 2015We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational ... More Badly approximable systems of affine formsAug 12 1998Jan 20 1999We prove an inhomogeneous analogue of W. M. Schmidt's (1969) theorem on Hausdorff dimension of the set of badly approximable systems of linear forms. The proof is based on ideas and methods from the theory of dynamical systems, in particular, on abundance ... More Diophantine exponents of measures: a dynamical approachJun 24 2005We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional Diophantine approximation ... More Beam-Beam Resonances for Different Collision SchemesJun 25 2008One of the main advantages of proposed by P. Raimondi "Crab Waist" collision scheme is a strong suppression of betatron resonances excited by beam-beam interaction. Some qualitative explanations with numerical examples, describing beam-beam resonances ... More On weak Lie 2-algebrasDec 20 2007A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between ... More A note on the residue Chern characterNov 09 2005The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth differential ... More On the replica symmetric solution of the K-sat modelApr 22 2013In this paper we translate Talagrand's solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions ... More