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Metal-insulator transition in the ground-state of the three-band Hubbard model at half-fillingJul 16 2018The three-band Hubbard model is a fundamental model for understanding properties of the Copper-Oxygen planes in cuprate superconductors. We use cutting-edge auxiliary-field quantum Monte Carlo (AFQMC) methods to investigate ground state properties of ... More

Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computationsMay 22 2017Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes ... More

Response functions for the two-dimensional ultracold Fermi gas: dynamical BCS theory and beyondJun 12 2017Nov 26 2017Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles like neutrons, or photons. Calculations of such ... More

Dynamical BCS theory of a two-dimensional attractive Fermi gas: effective interactions from Quantum Monte Carlo calculationsMay 14 2019The primary work presented in this paper focuses on the calculation of density-density dynamical correlations in an attractive two dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC-BCS crossover regime. ... More

Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approachesMay 08 2019We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving ... More

Stacks of Ann-Categories and their morphismsJan 29 2015Jul 07 2015We show that $\mathit{ann}$-categories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. More precisely, we prove the groupoid of morphisms between two $\mathit{ann}$-categories ... More

Toda Fields on Riemann Surfaces: remarks on the Miura transformationAug 05 1995We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of $W$--algebras are thus interpreted as partial ... More

Hermitian-holomorphic Deligne cohomology, Deligne pairing for singular metrics, and hyperbolic metricsAug 09 2004Aug 13 2004We introduce a model for Hermitian holormorphic Deligne cohomology on a projective algebraic manifold which allows to incorporate singular hermitian structures along a normal crossing divisor. In the case of a projective curve, the cup-product in cohomology ... More

Quantum dynamics and entanglement of a 1D Fermi gas released from a trapApr 16 2012We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of N particles is initially in the ground state within hard-wall or harmonic traps, then it expands after ... More

The Euclidean two-point correlation function of the topological charge densityJan 12 1999May 12 1999We study the Euclidean two-point correlation function $G_q(x)$ of the topological charge density in QCD. A general statement based on reflection positivity tells us that $G_q(x)<0$ for $x\neq 0 $. On the other hand the topological susceptibility $\chi_q=\int ... More

Monte Carlo simulation of lattice ${\rm CP}^{N-1}$ models at large NSep 28 1992In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models. Quantitative ... More

On hermitian-holomorphic classes related to uniformization, the dilogarithm, and the Liouville ActionNov 04 2002Jul 09 2004Metrics of constant negative curvature on a compact Riemann surface are critical points of the Liouville action functional, which in recent constructions is rigorously defined as a class in a Cech-de Rham complex with respect to a suitable covering of ... More

Critical phenomena and renormalization-group flow of multi-parameter Φ^4 field theoriesSep 07 2007Sep 17 2007In the framework of the renormalization-group (RG) approach, critical phenomena can be investigated by studying the RG flow of multi-parameter $\Phi^4$ field theories with an $N$-component fundamental field, containing up to 4th-order polynomials of the ... More

2-Gerbes bound by complexes of gr-stacks, and cohomologyDec 20 2005We define 2-gerbes bound by complexes of braided group-like stacks. We prove a classification result in terms of hypercohomology groups with values in abelian crossed squares and cones of morphisms of complexes of length 3. We give an application to the ... More

Biextensions, bimonoidal functors, multilinear functor calculus, and categorical ringsJan 19 2015Jul 31 2017We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of the kind of ... More

Entanglement and particle correlations of Fermi gases in harmonic trapsApr 10 2012We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations ... More

Biextensions, bimonoidal functors, multilinear functor calculus, and categorical ringsJan 19 2015Aug 06 2015We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of the kind of ... More

Hermitian-holomorphic (2)-Gerbes and tame symbolsOct 02 2003Oct 13 2004We observe that the line bundle associated to the tame symbol of two invertible holomorphic functions also carries a fairly canonical hermitian metric, hence it represents a class in a Hermitian holomorphic Deligne cohomology group. We put forward an ... More

Magnetic orders in the hole doped three-band Hubbard model: spin spirals, nematicity, and ferromagnetic domain wallsMay 15 2018Jun 01 2018The Copper-Oxygen planes in cuprates have been at the center of the search for a theory of high-temperature superconductivity. We conduct an extensive study of the ground state of the three-band Hubbard (Emery) model in the underdoped regime. We focus ... More

Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte CarloJun 15 2016Aug 23 2016We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although most of the calculations ... More

Abridged Petri NetsDec 10 2013A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, ... More

Perelman's Stability TheoremFeb 28 2007Mar 13 2007We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with curvature bounded below Gromov-Hausdorff converging to a compact Alexandrov space $X$, $X_i$ is homeomorphic to $X$ ... More

Formation of superheavy elements in heavy-ion collisionsOct 11 2001The cold fusion reactions related to 208Pb and 209Bi targets leading to superheavy elements (SHE) with Z=104-112 have been successfully considered in our model recently. Here we briefly discuss this model and extend our consideration to fusion reactions ... More

Quotients of the crown domain by a proper action of a cyclic groupAug 06 2012Let G/K be an irreducible Riemannian symmetric space of the non-compact type and denote by \Xi the associated crown domain. We show that for any proper action of a cyclic group \Gamma the quotient \Xi/\Gamma is Stein. An analogous statement holds true ... More

Curvature bounds via Ricci smoothingMay 29 2004We give a proof of the fact that the upper and the lower sectional curvature bounds of a complete manifold vary at a bounded rate under the Ricci flow.

Restrictions on collapsing with a lower sectional curvature boundOct 08 2001We obtain new topological information about the local structure of collapsing under a lower sectional curvature bound. As an application we prove a new sphere theorem and obtain a partial result towards the conjecture that not every Alexandrov space can ... More

Transition phenomena for ladder epochs of random walks with small negative driftMay 08 2009For a family of random walks $\{S^{(a)}\}$ satisfying $\mathbf{E}S_1^{(a)}=-a<0$ we consider ladder epochs $\tau^{(a)}=\min\{k\geq1: S_k^{(a)}<0\}$. We study the asymptotic, as $a\to0$, behaviour of $\mathbf{P}(\tau^{(a)}>n)$ in the case when $n=n(a)\to\infty$. ... More

Regularity of limits of noncollapsing sequences of manifoldsSep 11 2001We prove that iterated spaces of directions of a limit of a noncollapsing sequence of manifolds with lower curvature bound are topologically spheres. As an application we show that for any finite dimensional Alexandrov space $X^n$ with $n\ge 5$ there ... More

Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0Mar 05 2007We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the three-dimensional N-vector ... More

Interacting N-vector order parameters with O(N) symmetrySep 21 2004We consider the critical behavior of the most general system of two N-vector order parameters that is O(N) invariant. We show that it may a have a multicritical transition with enlarged symmetry controlled by the chiral O(2)xO(N) fixed point. For N=2, ... More

High-order perturbative expansions of multi-parameter Phi^4 quantum field theoriesDec 14 2007We present high-order pertubative expansions of multi-parameter Phi^4 quantum field theories with an N-component fundamental field, containing up to 4th-order polynomials of the field. Multi-parameter Phi^4 theories generalize the simplest O(N)-symmetric ... More

Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic fieldFeb 12 2007We study the phase diagram and multicritical behavior of anisotropic Heisenberg antiferromagnets on a square lattice in the presence of a magnetic field along the easy axis. We argue that, beside the Ising and XY critical lines, the phase diagram presents ... More

Off-equilibrium scaling behaviors across first-order transitionsAug 11 2015Aug 19 2015We study off-equilibrium behaviors at first-order transitions (FOTs) driven by a time dependence of the temperature across the transition point Tc, such as the linear behavior T(t)/Tc = 1 - t/ts where ts is a time scale. In particular, we investigate ... More

Comment on "Spurious fixed points in frustrated magnets," cond-mat/0609285Oct 04 2006We critically discuss the arguments reported in cond-mat/0609285 by B. Delamotte, Yu. Holovatch, D. Ivaneyko, D. Mouhanna, and M. Tissier. We show that their conclusions are not theoretically founded. They are contradicted by theoretical arguments and ... More

Twisted Eguchi-Kawai Reduced Chiral ModelsMar 18 2002We study the twisted Eguchi-Kawai (TEK) reduction procedure for large-N unitary matrix lattice models. In particular, we consider the case of two-dimensional principal chiral models, and use numerical Monte Carlo (MC) simulations to check the conjectured ... More

Simulating a CP-violating topological term in gauge theoriesDec 05 2011We present recent results on the theta-dependence of four-dimensional SU(N) gauge theories, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we study the scaling behavior of these theories, by Monte ... More

Schouten identities for Feynman graph amplitudes; the Master Integrals for the two-loop massive sunrise graphNov 13 2013Jan 28 2014A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two loop sunrise graph with arbitrary masses for recovering ... More

Critical dynamics in trapped particle systemsJul 05 2011We discuss the effects of a trapping space-dependent potential on the critical dynamics of lattice gas models. Scaling arguments provide a dynamic trap-size scaling framework to describe how critical dynamics develops in the large trap-size limit. We ... More

An Elliptic Generalization of Multiple PolylogarithmsSep 11 2017Oct 10 2017We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the \epsilon-expansion of the imaginary part of the two-loop massive sunrise graph. Building ... More

Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitionsDec 11 2012Dec 18 2012We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading ... More

Theta dependence of SU(N) gauge theories in the presence of a topological termMar 11 2008Feb 06 2013We review results concerning the theta dependence of 4D SU(N) gauge theories and QCD, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss theta dependence in the large-N limit. Most results ... More

Corrections to scaling in multicomponent polymer solutionsJan 30 2006We calculate the correction-to-scaling exponent $\omega_T$ that characterizes the approach to the scaling limit in multicomponent polymer solutions. A direct Monte Carlo determination of $\omega_T$ in a system of interacting self-avoiding walks gives ... More

Butterflies II: Torsors for 2-group stacksSep 18 2009Mar 19 2010We study torsors over 2-groups and their morphisms. In particular, we study the first non-abelian cohomology group with values in a 2-group. Butterfly diagrams encode morphisms of 2-groups and we employ them to examine the functorial behavior of non-abelian ... More

Toda Field Theory as a Clue to the Geometry of $W_n$--GravityNov 24 1994We discuss geometrical aspects of Toda Fields generalizing the links between Liouville gravity and uniformization of Riemann surfaces of genus greater than one. The framework is the interplay between the hermitian and the holomorphic geometry of vector ... More

Scaling of decoherence and energy flow in interacting quantum spin systemsMar 05 2019We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising ... More

Critical mass renormalization in renormalized phi4 theories in two and three dimensionsAug 05 2015We consider the O(N)-symmetric phi4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the phi4 continuum theory. The required nonperturbative information is obtained by resumming high-order perturbative ... More

Anisotropic perturbations in three-dimensional O(N)-symmetric vector modelsAug 02 2011We investigate the effects of anisotropic perturbations in three-dimensional O(N)-symmetric vector models. In order to assess their relevance for the critical behavior, we determine the renormalization-group dimensions of the anisotropic perturbations ... More

Equilibrium and nonequilibrium entanglement properties of 2D and 3D Fermi gasesJan 16 2013Mar 01 2013We investigate the entanglement properties of the equilibrium and nonequilibrium quantum dynamics of 2D and 3D Fermi gases, by computing entanglement entropies of extended space regions, which generally show multiplicative logarithmic corrections to the ... More

Three-dimensional ferromagnetic CP(N-1) modelsMay 08 2019May 10 2019We investigate the critical behavior of three-dimensional ferromagnetic CP(N-1) models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we find a critical ... More

Three-dimensional ferromagnetic CP(N-1) modelsMay 08 2019Aug 01 2019We investigate the critical behavior of three-dimensional ferromagnetic CP(N-1) models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we find a critical ... More

Cup products, the Heisenberg group, and codimension two algebraic cyclesOct 07 2015We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This generalization of the classical relation between divisors ... More

Relevance of the axial anomaly at the finite-temperature chiral transition in QCDSep 21 2013Jun 30 2015We investigate the nature of the finite-temperature chiral transition in QCD with two light flavors, in the case of an effective suppression of the the U(1)_A symmetry breaking induced by the axial anomaly, which implies the symmetry breaking U(2)_L X ... More

The 4D SU(3) gauge theory with an imaginary theta termSep 30 2011We study the scaling behavior of the 4D SU(3) lattice gauge theory in the presence of a theta term, by Monte Carlo simulations computing the topological properties at imaginary theta. The numerical results provide a good evidence of scaling in the continuum ... More

Critical Phenomena and Renormalization-Group TheoryDec 10 2000May 03 2002We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of self-avoiding walks. For ... More

Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's FunctionJan 25 1994Analytical and numerical methods are applied to principal chiral models on a two-dimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of SU(N) models are developed and applied to the evaluation ... More

Two dimensional SU(N) x SU(N) chiral models on the latticeJul 15 1993Sep 08 1993Lattice $SU(N)\times SU(N)$ chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. $12^{th}$ order strong coupling series for the free and internal energy are obtained for all $N\geq 6$. Three loop contributions ... More

Classical improvement of lattice actions and quantum effects: a unified viewJul 26 1996The possibility of removing the one-loop perturbative effects of lattice artifacts by a proper choice of the lattice action is explored, and found to depend crucially on the properties of the physical quantity considered. In this respect the finite-space-volume ... More

Quasi-long-range order in trapped systemsNov 20 2010We investigate the effects of a trapping space-dependent potential on the low-temperature quasi-long-range order phase of two-dimensional particle systems with a relevant U(1) symmetry, such as quantum atomic gases. We characterize the universal features ... More

Ground-state fidelity at first-order quantum transitionsJul 04 2018Nov 30 2018We analyze the scaling behavior of the fidelity, and the corresponding susceptibility, emerging in finite-size many-body systems whenever a given control parameter $\lambda$ is varied across a quantum phase transition. For this purpose we consider a finite-size ... More

Low-density phases of $^3$He monolayers adsorbed on graphiteDec 12 2015Feb 10 2016Quantum Monte Carlo simulations at zero temperature of a $^3$He monolayer adsorbed on graphite, either clean or preplated with $^4$He, unexpectedly point to a gas-liquid phase transition at a very low areal density of the order of 0.01\AA$^{-2}$. This ... More

Using Parity Kicks for Decoherence ControlAug 26 1998Mar 10 1999We show how it is possible to suppress decoherence using tailored external forcing acting as pulses. In the limit of infinitely frequent pulses decoherence and dissipation are completely frozen; however, a significant decoherence suppression is already ... More

Alternative constructions of a harmonic function for a random walk in a coneMay 03 2018May 25 2019For a random walk killed at leaving a cone we suggest two new constructions of a positive harmonic function. These constructions allow one to remove a quite strong extendability assumption, which has been imposed in our previous paper (Denisov and Wachtel, ... More

Topological obstructions to nonnegative curvatureJan 24 2000We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively ... More

Invariance principles for random walks in conesAug 31 2015Nov 01 2015We prove invariance principles for a mulditimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of $h$-transformed random walk ... More

Local asymptotics for the area under the random walk excursionAug 21 2017We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and light-tailed increments. We determine the asymptotics for local probabilities for the area and prove a local central limit ... More

Martingale approach to subexponential asymptotics for random walksNov 29 2011Consider the random walk $S_n=\xi_1+...+\xi_n$ with independent and identically distributed increments and negative mean $\mathbf E\xi=-m<0$. Let $M=\sup_{0\le i} S_i$ be the supremum of the random walk. In this note we present derivation of asymptotics ... More

Random walks in conesOct 06 2011Jun 03 2015We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof ... More

α-concave functions and a functional extension of mixed volumesFeb 04 2013Mixed volumes, which are the polarization of volume with respect to the Minkowski addition, are fundamental objects in convexity. In this note we announce the construction of mixed integrals, which are functional analogs of mixed volumes. We build a natural ... More

Pinching estimates for negatively curved manifolds with nilpotent fundamental groupsMay 30 2004Aug 28 2010Let $M$ be a complete Riemannian metric of sectional curvature within $[-a^2,-1]$ whose fundamental group contains a $k$-step nilpotent subgroup of finite index. We prove that $a\ge k$ answering a question of M. Gromov. Furthermore, we show that for any ... More

Biquotients with singly generated rational cohomologyOct 16 2002Jun 26 2017We classify all biquotients whose rational cohomology rings are generated by one element. As a consequence we show that the Gromoll-Meyer 7-sphere is the only exotic sphere which can be written as a biquotient.

Finiteness theorems for nonnegatively curved vector bundlesFeb 03 2000We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds whose topology is concentrated on compact domains of ``bounded geometry''. ... More

Manifolds without conjugate points and their fundamental groupsMay 20 2012We show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split.

Reservoir engineering of a mechanical resonator: generating a macroscopic superposition state and monitoring its decoherenceAug 01 2013Oct 26 2013A deterministic scheme for generating a macroscopic superposition state of a nanomechanical resonator is proposed. The nonclassical state is generated through a suitably engineered dissipative dynamics exploiting the optomechanical quadratic interaction ... More

Direct Numerical Simulations of Low-$Rm$ MHD turbulence based on the least dissipative modesFeb 09 2010We present a new spectral method for the Direct Numerical Simulation of Magnetohydrodynamic turbulence at low Magnetic Reynolds number. The originality of our approach is that instead of using traditional bases of functions, it relies on the basis of ... More

Obstructions to nonnegative curvature and rational homotopy theoryJul 01 2000Nov 15 2002We establish a link between rational homotopy theory and the problem which vector bundles admit complete Riemannian metric of nonnegative sectional curvature. As an application, we show for a large class of simply-connected nonnegatively curved manifolds ... More

Exact asymptotics for the instant of crossing a curve boundary by an asymptotically stable random walkMar 24 2014Suppose that $\{S_n,\ n\geq0\}$ is an asymptotically stable random walk. Let $g$ be a positive function and $T_g$ be the first time when $S_n$ leaves $[-g(n),\infty)$. In this paper we study asymptotic behaviour of $T_g$. We provide integral tests for ... More

Heavy-traffic analysis of the maximum of an asymptotically stable random walkFeb 12 2009For families of random walks $\{S_k^{(a)}\}$ with $\mathbf E S_k^{(a)} = -ka < 0$ we consider their maxima $M^{(a)} = \sup_{k \ge 0} S_k^{(a)}$. We investigate the asymptotic behaviour of $M^{(a)}$ as $a \to 0$ for asymptotically stable random walks. ... More

Obstructions to nonnegative curvature and rational homotopy theoryJul 01 2000Sep 07 2017We establish a link between rational homotopy theory and the problem which vector bundles admit complete Riemannian metric of nonnegative sectional curvature. As an application, we show for a large class of simply-connected nonnegatively curved manifolds ... More

Universality of local times of killed and reflected random walksDec 18 2014In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential distribution. ... More

Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursionJul 04 2019This note is devoted to the study of the maximum of the excursion of a random walk with negative drift and light-tailed increments. More precisely, we determine the local asymptotics of the joint distribution of the length, maximum and the time at which ... More

Green function of a random walk in a coneJul 19 2018This paper studies the asymptotic behavior of the Green function of a multidimensional random walk killed when leaving a convex cone with smooth boundary. Our results imply uniqueness, up to a multiplicative factor, of the positive harmonic function for ... More

Mixed integrals and related inequalitiesOct 16 2012In this paper we define an addition operation on the class of quasi-concave functions. While the new operation is similar to the well-known sup-convolution, it has the property that it polarizes the Lebesgue integral. This allows us to define mixed integrals, ... More

Implementation of a three-qubit quantum error correction code in a cavity-QED setupMay 17 2010Jul 05 2010The correction of errors is of fundamental importance for the development of contemporary computing devices and of robust communication protocols. In this paper we propose a scheme for the implementation of the three-qubit quantum repetition code, exploiting ... More

Biquotients with singly generated rational cohomologyOct 16 2002We classify all biquotients whose rational cohomology rings are generated by one element. As a consequence we show that the Gromoll-Meyer 7-sphere is the only exotic sphere which can be written as a biquotient.

Decoherence Control for Optical QubitsFeb 12 1998Photons in cavities have been already used for the realization of simple quantum gates [Q.A. Turchette, Phys. Rev. Lett. 75,4710 (1995)]. We present a method for combatting decoherence in this case.

Multifractal analysis of superprocesses with stable branching in dimension oneDec 03 2012Nov 17 2015We show that density functions of a $(\alpha,1,\beta)$-superprocesses are almost sure multifractal for $\alpha>\beta+1$, $\beta\in(0,1)$ and calculate the corresponding spectrum of singularities.

Phase noise measurement in a cavity with a movable mirror undergoing quantum Brownian motionJun 19 2000Oct 19 2000We study the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion. We study the phase noise power spectrum of the output light, and we describe the mirror Brownian motion, which is responsible for the thermal ... More

Optimal fidelity of teleportation of coherent states and entanglementAug 20 2008Jan 02 2009We study the Braunstein-Kimble protocol for the continuous variable teleportation of a coherent state. We determine lower and upper bounds for the optimal fidelity of teleportation, maximized over all local Gaussian operations for a given entanglement ... More

On the topology and the boundary of N-dimensional RCD(K,N) spacesJul 04 2019Aug 04 2019We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, ... More

Local limit theorems for ladder epochsJan 31 2007Let {S_n, n=0,1,2,...} be a random walk generated by a sequence of i.i.d. random variables X_1, X_2,... and let tau be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an alpha-stable law, ... More

CD meets CATDec 07 2017Jan 20 2018We show that if a noncollapsed $CD(K,n)$ space $X$ with $n\ge 2$ has curvature bounded above by $\kappa$ in the sense of Alexandrov then $K\le (n-1)\kappa$ and $X$ is an Alexandrov space of curvature bounded below by $K-\kappa (n-2)$. We also show that ... More

On dimensions of tangent cones in limit spaces with lower Ricci curvature boundsJun 09 2015Oct 27 2015We show that if $X$ is a limit of $n$-dimensional Riemannian manifolds with Ricci curvature bounded below and $\gamma$ is a limit geodesic in $X$ then along the interior of $\gamma$ same scale measure metric tangent cones $T_{\gamma(t)}X$ are H\"older ... More

Existence and approximation of Hunt processes associated with generalized Dirichlet formsMar 16 2011Nov 05 2011We show that any strictly quasi-regular generalized Dirichlet form that satisfies the mild structural condition D3 is associated to a Hunt process, and that the associated Hunt process can be approximated by a sequence of multivariate Poisson processes. ... More

Exit times for integrated random walksJul 10 2012We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time $n$. Assuming that the moment of order $2+\delta$ is finite, we show ... More

Ordered random walks with heavy tailsMar 23 2011This note continues paper of Denisov and Wachtel (2010), where we have constructed a $k$-dimensional random walk conditioned to stay in the Weyl chamber of type $A$. The construction was done under the assumption that the original random walk has $k-1$ ... More

Topics in Geometric Group Theory. Part IApr 14 2018This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of easy groups. ... More

On noncollapsed almost Ricci-flat 4-manifoldsJun 29 2016Jul 23 2016We give topological conditions to ensure that a noncollapsed almost Ricci-flat 4-manifold admits a Ricci-flat metric. One sufficient condition is that the manifold is spin and has a nonzero A-hat genus. Another condition is that the fundamental group ... More

On the topology and the boundary of N-dimensional RCD(K,N) spacesJul 04 2019We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, ... More

Lower deviation probabilities for supercritical Galton-Watson processesMay 31 2005There is a well-known sequence of constants c_n describing the growth of supercritical Galton-Watson processes Z_n. With 'lower deviation probabilities' we refer to P(Z_n=k_n) with k_n=o(c_n) as n increases. We give a detailed picture of the asymptotic ... More

Fractional Cable Model for Signal Conduction in Spiny Neuronal DendritesFeb 17 2017The cable model is widely used in several fields of science to describe the propagation of signals. A relevant medical and biological example is the anomalous subdiffusion in spiny neuronal dendrites observed in several studies of the last decade. Anomalous ... More