Results for "Dmitry K. Efimkin"
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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 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 Kinetic theory of dark solitons with tunable frictionMar 02 2017May 04 2017We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a non-interacting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of ... More 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 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 Zero Energy Ground State in the Three-Body SystemDec 02 2009Jan 22 2010We consider a 3--body system in $\mathbb{R}^3$ with non--positive potentials and non--negative essential spectrum. Under certain requirements on the fall off of pair potentials it is proved that if at least one pair of particles has a zero energy resonance ... 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 Bound States at Threshold resulting from Coulomb RepulsionDec 06 2011Oct 22 2012The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction on the particle ... More Zero Energy Bound States and Resonances in Three--Particle SystemsNov 29 2011Apr 16 2012We consider a three-particle system in $\mathbb{R}^3$ with non-positive pair-potentials and non-negative essential spectrum. Under certain restrictions on potentials it is proved that the eigenvalues are absorbed at zero energy threshold given that there ... More 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 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 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 Coherent phase slips in superconducting nanoringsJul 15 2011We study quantum fluctuations of persistent current in a small superconducting ring. Based on a microscopic model of the ring we argue that under certain conditions such ring will exhibit coherent quantum phase slips, similar to those in a flux qubit. ... More Cold Atom QubitsMay 29 2010Dec 20 2010We discuss a laser-trapped cold-atom superfluid qubit system. Each qubit is proposed as a macroscopic two-state system based on a set of Bose-Einstein condensate (BEC) currents circulating in a ring, cut with a Josephson barrier. We review the effective ... 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 Collective excitations on a surface of topological insulatorOct 18 2011We study collective excitations in a helical electron liquid on a surface of three-dimensional topological insulator. Electron in helical liquid obeys Dirac-like equation for massless particless and direction of its spin is strictly determined by its ... More Electron-hole pairing in topological insulator thin filmJul 07 2012Sep 01 2012We consider pairing of massless Dirac electrons and holes located on opposite surfaces of thin film of "strong" three-dimensional topological insulator. Such pairing was predicted to give rise to topological exciton condensate with unusual properties. ... More Complexity of regular abstractions of one-counter languagesFeb 10 2016We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L(A): its (1) downward ... More Reaction kinetics of ultracold molecule-molecule collisionsMay 21 2018Studying chemical reactions on a state-to-state level tests and improves our fundamental understanding of chemical processes. For such investigations it is convenient to make use of ultracold atomic and molecular reactants as they can be prepared in well ... 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 Higher Airy structures, W algebras and topological recursionDec 20 2018Mar 29 2019We define higher quantum Airy structures as generalizations of the Kontsevich-Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of higher quantum ... 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 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 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 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 Free energy in the mixed p-spin models with vector spinsDec 14 2015Dec 27 2015Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which include the ... More Free energy in the Potts spin glassDec 01 2015Nov 11 2016We 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 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 Tauberian theorem for value functionsJul 20 2016Apr 10 2017For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value functions of $\lambda$-discounted ... More Variational solutions to the abstract Euler equationMay 15 2019We study a class of nonlinear evolutionary equations of a certain structure reminiscent of the incompressible Euler equations. This includes, in particular, the ideal MHD, multidimensional Camassa-Holm, EPDiff, Euler-alpha and Korteweg-de Vries equations, ... More Algebraization of a Cartier divisorOct 15 2012We extend to pairs classical results of R. Elkik on lifting of homomorphisms and algebraization. In particular, we establish algebraization of an affine rig-smooth formal variety with a rig-smooth closed subvariety. This solves affirmatively a problem ... More Device physics of van der Waals heterojunction solar cellsMar 07 2019Heterostructures based on atomically thin semiconductors are considered a promising emerging technology for the realization of ultrathin and ultralight photovoltaic solar cells on flexible substrates. Much progress has been made in recent years on a technological ... More Optical imaging of strain in two-dimensional crystalsMar 07 2019Strain engineering is widely used in material science to tune the (opto-)electronic properties of materials and enhance the performance of devices. Two-dimensional atomic crystals are a versatile playground to study the influence of strain, as they can ... More Interest rate models and Whittaker functionsMay 10 2014I present the technique which can analyse some interest rate models: Constantinides-Ingersoll, CIR-model, geometric CIR and Geometric Brownian Motion. All these models have the unified structure of Whittaker function. The main focus of this text is closed-form ... More The closed-open string map for $S^1$-invariant LagrangiansApr 07 2015Given a monotone Lagrangian submanifold invariant under a loop of Hamiltonian diffeomorphisms, we compute a piece of the closed-open string map into the Hochschild cohomology of the Lagrangian which captures the homology class of the loop's orbit on that ... More Restricted trichotomy in higher dimensionsApr 19 2016Apr 27 2016I prove, answering a question of Zilber, that if $M$ is an algebraic variety of dimension strictly greater than one and $(M, \ldots)$ is a strongly minimal structure with atomic relations definable in the Zariski language on $M$, then $M$ is locally modular. ... More Block-diagonalization of matrices over local rings.IINov 24 2014Consider rectangular matrices over a local ring R. In the previous work we have obtained criteria for block-diagonalization of such matrices, i.e. U A V=A_1\oplus A_2, where U,V are invertible matrices over R. In this short note we extend the criteria ... More The Axion Dark Matter eXperimentDec 06 2011The Axion is a particle arising from the Peccei-Quinn solution to the strong CP problem. Peccei-Quinn symmetry breaking in the early universe could produce a large number of axions which would still be present today, making the axion a compelling dark ... More Continuous averaging in dynamical systemsApr 28 2003The method of continuous averaging can be regarded as a combination of the Lie method, where a change of coordinates is constructed as a shift along solutions of a differential equation and the Neishtadt method, well-known in perturbation theory for ODE ... More Real-time High Resolution Fusion of Depth Maps on GPUNov 28 2013A system for live high quality surface reconstruction using a single moving depth camera on a commodity hardware is presented. High accuracy and real-time frame rate is achieved by utilizing graphics hardware computing capabilities via OpenCL and by using ... More Order complexes of noncomplemented lattices are nonevasiveApr 28 1997We reprove and generalize in a combinatorial way the result of A. Bj\"orner [J.\ Comb.\ Th.\ A {\bf 30}, 1981, pp.~90--100, Theorem 3.3], that order complexes of noncomplemented lattices are contractible, namely by showing that these simplicial complexes ... More The flashing ratchet and unidirectional transport of matterMar 17 2010Sep 17 2010We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor really performs unidirectional ... More On Barnes Beta Distributions, Selberg Integral and Riemann XiFeb 25 2014The theory of Barnes beta probability distributions is advanced and related to the Riemann xi function. The scaling invariance, multiplication formula, and Shintani factorization of Barnes multiple gamma functions are reviewed using the approach of Ruijsenaars ... More