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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

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

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

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

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

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

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

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

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

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

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

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

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 driven by time-dependent external fields in three-dimensional O(N) vector modelsDec 19 2015Mar 07 2016We consider the dynamical off-equilibrium behavior of the three-dimensional O$(N)$ vector model in the presence of a slowly-varying time-dependent spatially-uniform magnetic field ${\bm H}(t) = h(t)\,{\bm e}$, where ${\bm e}$ is a $N$-dimensional constant ... 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

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

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

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

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

Equilibrium and off-equilibrium trap-size scaling in 1D ultracold bosonic gasesOct 05 2010Jan 03 2011We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with increasing the trap ... More

Trap-size scaling in confined particle systems at quantum transitionsJun 15 2009Feb 03 2010We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian ... 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

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

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

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

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

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.

Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantizationJan 09 1998Strong and Markov uniqueness problems in $L^2$ for Dirichlet operators on rigged Hilbert spaces are studied. An analytic approach based on a--priori estimates is used. The extension of the problem to the $L^p$-setting is discussed. As a direct application ... More

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

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

Regularity and irregularity of superprocesses with $(1+β)$-stable branching mechanismAug 09 2015We would like to give an overview of results on regularity, or better to say "irregularity", properties of densities at fixed times of super-Brownian motion with $(1+\beta)$-stable branching for $\beta<1$. First, the following dichotomy for the density ... 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

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

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

Failure mechanisms of load sharing complex systemsNov 26 2013Jan 30 2014We investigate the failure mechanisms of load sharing complex systems. The system is composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and demand respectively) ... 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

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

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

Upper bounds for the maximum of a random walk with negative driftJul 27 2011Consider a random walk $S_n=\sum_{i=0}^n X_i$ with negative drift. This paper deals with upper bounds for the maximum $M=\max_{n\ge 1}S_n$ of this random walk in different settings of power moment existences. As it is usual for deriving upper bounds, ... 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

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

Large deviations for sums defined on a Galton-Watson processMay 23 2006In this paper we study the large deviation behavior of sums of i.i.d. random variables X_i defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX_1^2 and EZ_1log Z_1. The underlying interplay of the partial sums ... More

Feedback-assisted ponderomotive squeezingNov 19 2010Dec 11 2010We analyze how the radiation pressure interaction between a mechanical element and an intensely driven optical cavity mode can be exploited for generating squeezed light. We study in particular how the performance of the optomechanical device can be improved ... More

Heating and decoherence suppression using decoupling techniquesAug 01 2001Sep 25 2001We study the application of decoupling techniques to the case of a damped vibrational mode of a chain of trapped ions, which can be used as a quantum bus in linear ion trap quantum computers. We show that vibrational heating could be efficiently suppressed ... 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.

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

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

Fixed point stability and decay of correlationsNov 14 2006In the framework of the renormalization-group theory of critical phenomena, a quantitative description of many continuous phase transitions can be obtained by considering an effective $\Phi^4$ theories, having an N-component fundamental field $\Phi_i$ ... More

Generating Functional in CFT on Riemann Surfaces II: Homological AspectsJun 20 2000We revisit and generalize our previous algebraic construction of the chiral effective action for Conformal Field Theory on higher genus Riemann surfaces. We show that the action functional can be obtained by evaluating a certain Deligne cohomology class ... More

Finitely presented groups and the Whitehead nightmareOct 09 2014Mar 21 2016We define a `nice representation' of a finitely presented group G as being a non-degenerate essentially surjective simplicial map f from a `nice' space X into a 3-complex associated to a presentation of G, with a strong control over the singularities ... 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

Notes on Weak Units of Group-Like 1- and 2-StacksAug 09 2011Sep 30 2015The weak units of strict monoidal 1- and 2-categories are already defined. In this paper, we define them for group-like 1- and 2-stacks. We show that they form a contractible Picard 1- and 2-stack, respectively. We give their cohomological description ... More

Shock (Blast) Mitigation by "Soft" Condensed MatterMar 18 2003Aug 24 2007It is a common point that "soft" condensed matter (like granular materials or foams) can reduce damage caused by impact or explosion. It is attributed to their ability to absorb significant energy. This is certainly the case for a quasistatic type of ... 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

Phonon Josephson Junction with Nanomechanical ResonatorsJan 08 2016Mar 07 2016We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction which exhibits two different dynamical ... More

Chaos, Thermodynamics and Quantum Mechanics: an Application to Celestial DynamicsJun 29 1998Sep 07 1998We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the planetary motion is ... More

Solvability Conditions for Some non Fredholm OperatorsFeb 18 2009We obtain solvability conditions for some elliptic equations involving non Fredholm operators with the methods of spectral theory and scattering theory for Schrodinger type operators. Though the Fredholm property is not satisfied, the solvability conditions ... More

Structure of fundamental groups of manifolds with Ricci curvature bounded belowMay 30 2011Nov 02 2011Verifying a conjecture of Gromov we establish a generalized Margulis Lemma for manifolds with lower Ricci curvature bound. Among the various applications are finiteness results for fundamental groups of compact $n$-manifolds with upper diameter and lower ... More

Classification of negatively pinched manifolds with amenable fundamental groupsFeb 17 2004Aug 28 2010We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the M\"obius band, and the products of a line with the total spaces of flat vector bundles over closed infranilmanifolds. ... 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