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Dynamical many-body phases of the parametrically driven, dissipative Dicke modelJan 28 2015The dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a time-dependent parametric modulation of ... More

Topological Equivalence between the Fibonacci Quasicrystal and the Harper ModelApr 16 2012Sep 13 2012One-dimensional quasiperiodic systems, such as the Harper model and the Fibonacci quasicrystal, have long been the focus of extensive theoretical and experimental research. Recently, the Harper model was found to be topologically nontrivial. Here, we ... More

Enhanced compressibility due to repulsive interaction in the Harper modelNov 19 2013We study the interplay between repulsive interaction and an almost staggered on-site potential in one-dimension. Specifically, we address the Harper model for spinless fermions with nearest-neighbor repulsion, close to half-filling. Using density matrix ... More

Standard and Null Weak ValuesApr 05 2013Weak value (WV) is a quantum mechanical measurement protocol, proposed by Aharonov, Albert, and Vaidman. It consists of a weak measurement, which is weighed in, conditional on the outcome of a later, strong measurement. Here we define another two-step ... More

Controlled-NOT for multiparticle qubits and topological quantum computation based on parity measurementsAug 08 2007Jan 25 2008We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins-1/2 or in equivalent ... More

Comment on "Topological equivalence of crystal and quasicrystal band structures"Aug 11 2013Madsen et al. [arXiv:1307.2577] claim that one-dimensional insulating crystals and one-dimensional insulating quasicrystals are topologically equivalent and, thus, trivial. In this comment, we clarify that in topological classification of one-dimensional ... More

Four-Dimensional Quantum Hall Effect in a Two-Dimensional QuasicrystalFeb 11 2013Nov 25 2013One-dimensional (1D) quasicrystals exhibit physical phenomena associated with the 2D integer quantum Hall effect. Here, we transcend dimensions and show that a previously inaccessible phase of matter --- the 4D integer quantum Hall effect --- can be incorporated ... More

Charge sensing amplification via weak values measurementSep 23 2010Feb 24 2011A protocol employing weak values (WVs) to obtain ultra sensitive amplification of weak signals in the context of a solid state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly ... More

Measuring cotunneling in its wakeMar 24 2014Nov 26 2014We introduce a rate formalism to treat classically forbidden electron transport through a quantum dot (cotunneling) in the presence of a coupled measurement device. We demonstrate this formalism for a toy model case of cotunneling through a single-level ... More

Null weak values in multi-level systemsApr 05 2013A two-step measurement protocol of a quantum system, known as weak value (WV), has been introduced more than two decades ago by Aharonov et al. [1], and has since been studied in various contexts. Here we discuss another two-step measurement protocol ... More

Many-body manifestation of interaction-free measurement: the Elitzur-Vaidman bombDec 03 2015We consider an implementation of the Elitzur-Vaidman bomb experiment in a DC-biased electronic Mach-Zehnder interferometer with a leakage port on one of its arms playing the role of a "lousy bom". Many-body correlations tend to screen out manifestations ... More

Ultrasensitive hysteretic force sensing with parametric nonlinear oscillatorsMar 24 2016We propose a novel method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from ... More

Hanbury Brown and Twiss Correlations in Quantum Hall SystemsSep 25 2013Jan 03 2014We study a Hanbury Brown and Twiss (HBT) interferometer formed with chiral edge channels of a quantum Hall system. HBT cross-correlations are calculated for a device operating both in the integer and fractional quantum Hall regimes, the latter at Laughlin ... More

A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical SuperlatticeJul 08 2015More than 30 years ago, Thouless introduced the concept of a topological charge pump that would enable the robust transport of charge through an adiabatic cyclic evolution of the underlying Hamiltonian. In contrast to classical transport, the transported ... More

A quantum transducer using a parametric driven-dissipative phase transitionJan 10 2019We study a dissipative Kerr-resonator subject to both single- and two-photon detuned drives. Beyond a critical detuning threshold, the Kerr resonator exhibits a semiclassical first-order dissipative phase transition between two different steady-states, ... More

Paired Orbitals for Different Spins equationsApr 07 2008Eigenvalue-type equations for Lowdin-Amos-Hall spin-paired (corresponding) orbitals are developed to provide an alternative to the standard spin-polarized Hartree-Fock or Kohn-Sham equations. Obtained equations are non-canonical unrestricted Hartree-Fock-type ... More

Topological States and Adiabatic Pumping in QuasicrystalsSep 27 2011Sep 17 2012The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit ... More

Four-Dimensional Quantum Hall Effect with Ultracold AtomsMay 17 2015Jan 29 2016We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged ... More

Hanbury-Brown and Twiss interference of anyonsApr 10 2012Aug 20 2012We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin ... More

Topological Pumping over a Photonic Fibonacci QuasicrystalMar 27 2014Quasiperiodic lattices have recently been shown to be a non-trivial topological phase of matter. Charge pumping -- one of the hallmarks of topological states of matter -- was recently realized for photons in a one-dimensional (1D) off-diagonal Harper ... More

Measurement back-action in stacked graphene quantum dotsFeb 27 2016We present an electronic transport experiment in graphene where both classical and quantum mechanical charge detector back-action on a quantum dot are investigated. The device consists of two stacked graphene quantum dots separated by a thin layer of ... More

Fluctuation induced attraction between adhesion sites of supported membranesMar 07 2010We use scaling arguments and coarse grained Monte Carlo simulations to study the fluctuation mediated interactions between a pair of adhesion sites of a bilayer membrane and a supporting surface. We find that the potential of mean force is an infinitely ... More

Observation of Topological Phase Transitions in Photonic QuasicrystalsNov 19 2012Feb 15 2013Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the ... More

Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physicsOct 13 2015Apr 23 2016Recent technological advances in integrated photonics have spurred on the study of topological phenomena in engineered bosonic systems. Indeed, the controllability of silicon ring-resonator arrays has opened up new perspectives for building lattices for ... More

Nonequilibrium effects in the tunneling conductance spectra of small metallic particlesDec 18 1998The tunneling spectra of small metallic grains shows an unusual structure of the differential conductance peaks. Namely, resonance peaks appear in clusters, or develop substructure as the the gate voltage is changed. These features are manifestations ... More

Mode excitation Monte Carlo simulations of mesoscopically large membranesApr 09 2008Solvent-free coarse grained models represent one of the most promising approaches for molecular simulations of mesoscopically large membranes. In these models, the size of the simulated membrane is limited by the slow relaxation time of longest bending ... More

Mechanical surface tension governs membrane thermal fluctuationsNov 01 2011Motivated by the still ongoing debate about the various possible meanings of the term surface tension of bilayer membranes, we present here a detailed discussion that explains the differences between the "intrinsic", "renormalized", and "mechanical" tensions. ... More

Scaling limits of loop-erased random walks and uniform spanning treesApr 05 1999Apr 18 1999The uniform spanning tree (UST) and the loop-erased random walk (LERW) are related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the mesh goes to zero. Although the existence of scaling limits is still ... More

A Note on Koldobsky's Lattice Slicing InequalityAug 17 2016$ \newcommand{\R}{{\mathbb{R}}} \newcommand{\Z}{{\mathbb{Z}}} \renewcommand{\vec}[1]{{\mathbf{#1}}} $We show that if $K \subset \R^d$ is an origin-symmetric convex body, then there exists a vector $\vec{y} \in \Z^d$ such that \begin{align*} |K \cap \Z^d ... More

Membrane fluctuations near a plane rigid surfaceOct 23 2008We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface. Our analysis ... More

A percolation formulaJul 13 2001Jul 30 2001Let $A$ be an arc on the boundary of the unit disk $U$. We prove an asymptotic formula for the probability that there is a percolation cluster $K$ for critical site percolation on the triangular grid in $U$ which intersects $A$ and such that 0 is surrounded ... More

Information Theoretic Approach to Social NetworksJul 30 2014We propose an information theoretic model for sociological networks. The model is a microcanonical ensemble of states and particles. The states are the possible pairs of nodes (i.e. people, sites and alike) which exchange information. The particles are ... More

Conformally invariant scaling limits (an overview and a collection of problems)Feb 08 2006Feb 10 2006Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models. Only recently ... More

"Water-free" computer model for fluid bilayer membranesApr 09 2003We use a simple and efficient computer model to investigate the physical properties of bilayer membranes. The amphiphilic molecules are modeled as short rigid trimers with finite range pair interactions between them. The pair potentials have been designed ... More

Stress-constrained continuum topology optimization: a new approach based on elasto-plasticityAug 23 2016A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This is achieved ... More

Hyperfinite graph limitsNov 24 2007G\'abor Elek introduced the notion of a hyperfinite graph family: a collection of graphs is hypefinite if for every $\epsilon>0$ there is some finite $k$ such that each graph $G$ in the collection can be broken into connected components of size at most ... More

Algorithmic Verification of Continuous and Hybrid SystemsFeb 27 2014We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite ... More

A diagrammatic approach for open chaotic systemsJun 24 1999A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving Wigner representations ... More

Viscous fingering in volatile thin filmsSep 02 2008Feb 23 2009A thin water film on a cleaved mica substrate undergoes a first order phase transition between two values of film thickness. By inducing a finite evaporation rate of the water, the interface between the two phases develops a fingering instability similar ... More

Statistics of photodissociation spectra: nonuniversal propertiesDec 15 1998Jul 28 1999We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping resonances, a formula ... More

Statistical thermodynamics of adhesion points in supported membranesJul 26 2011Supported lipid membranes are useful and important model systems for studying cell membrane properties and membrane mediated processes. One attractive application of supported membranes is the design of phantom cells exhibiting well defined adhesive properties ... More

Combinatorically Prescribed Packings and Applications to Conformal and Quasiconformal MapsSep 05 2007The Andreev-Thurston Circle Packing Theorem is generalized to packings of convex bodies in planar simply connected domains. This turns out to be a useful tool for constructing conformal and quasiconformal mappings with interesting geometric properties. ... More

Compositions of random transpositionsApr 20 2004Jul 04 2007Let $Y=(y_1,y_2,...)$, $y_1\ge y_2\ge...$, be the list of sizes of the cycles in the composition of $c n$ transpositions on the set $\{1,2,...,n\}$. We prove that if $c>1/2$ is constant and $n\to\infty$, the distribution of $f(c)Y/n$ converges to PD(1), ... More

Anion-radical oxygen centers in small (AgO)n clusters: density functional theory predictionsDec 04 2012Anion-radical form of the oxygen centers O(-) is predicted at the DFT level for small silver oxide particles having the AgO stoichiometry. Model clusters (AgO)n appear to be ferromagnetic with appreciable spin density at the oxygen centers. In contrast ... More

Null Values and Quantum State DiscriminationMay 17 2012Apr 27 2013We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known ... More

Average kissing numbers for non-congruent sphere packingsMay 13 1994The Koebe circle packing theorem states that every finite planar graph can be realized as the nerve of a packing of (non-congruent) circles in R^3. We investigate the average kissing number of finite packings of non-congruent spheres in R^3 as a first ... More

Using Interactive Information Labels to Assist Decision Making Under Uncertainty: The Case for Long-term SavingJul 17 2015Jan 20 2016Product information labels can help users understand complex information leading them to make better decisions. One area where consumers are particularly prone to make costly decision-making errors is long-term saving, which requires understanding of ... More

Nucleosynthesis of r-Process Elements by Jittering Jets in Core-Collapse SupernovaeOct 03 2011Nov 30 2011We calculate the nucleosynthesis inside the hot bubble formed in the jittering-jets model for core collapse supernovae (CCSNe) explosions, and find the formation of several times 10^-4 M_\odot of r-process elements. In the jittering-jets model fast jets ... More

Projecting the Kondo Effect: Theory of the Quantum MirageJun 28 2000Jan 11 2001A microscopic theory is developed for the projection (quantum mirage) of the Kondo resonance from one focus of an elliptic quantum corral to the other focus. The quantum mirage is shown to be independent of the size and the shape of the ellipse, and experiences ... More

The leading Ruelle resonances of chaotic mapsMay 16 2000The leading Ruelle resonances of typical chaotic maps, the perturbed cat map and the standard map, are calculated by variation. It is found that, excluding the resonance associated with the invariant density, the next subleading resonances are, approximately, ... More

On the scaling limits of planar percolationJan 30 2011Dec 28 2011We prove Tsirelson's conjecture that any scaling limit of the critical planar percolation is a black noise. Our theorems apply to a number of percolation models, including site percolation on the triangular grid and any subsequential scaling limit of ... More

Statistical mechanics of bilayer membrane with a fixed projected areaJul 09 2003The equilibrium and fluctuation methods for determining the surface tension, $\sigma$, and bending modulus, $\kappa$, of a bilayer membrane with a fixed projected area are discussed. In the fluctuation method the elastic coefficients $\sigma$ and $\kappa$ ... More

Elasticity of Gaussian and nearly-Gaussian phantom networksJun 01 2000We study the elastic properties of phantom networks of Gaussian and nearly-Gaussian springs. We show that the stress tensor of a Gaussian network coincides with the conductivity tensor of an equivalent resistor network, while its elastic constants vanish. ... More

Coarse grained molecular simulations of membrane adhesion domainsJun 22 2014We use a coarse grained molecular model of supported lipid bilayers to study the formation of adhesion domains. We find that this process is a first order phase transition, triggered by a combination of pairwise short range attractive interactions between ... More

Duty-ratio of cooperative molecular motorsJan 22 2012Molecular motors are found throughout the cells of the human body, and have many different and important roles. These micro-machines move along filament tracks, and have the ability to convert chemical energy into mechanical work that powers cellular ... More

Statistical physics of power fluctuations in mode locked lasersDec 14 2008We present an analysis of the power fluctuations in the statistical steady state of a passively mode locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical physics problem, ... More

A Counterexample to Monotonicity of Relative Mass in Random WalksJun 29 2015Dec 13 2015For a finite undirected graph $G = (V,E)$, let $p_{u,v}(t)$ denote the probability that a continuous-time random walk starting at vertex $u$ is in $v$ at time $t$. In this note we give an example of a Cayley graph $G$ and two vertices $u,v \in G$ for ... More

Casimir forces in a T operator approachJul 26 2007Dec 21 2008We explore the scattering approach to Casimir forces. Our main tool is the description of Casimir energy in terms of transition operators, as presented in Kenneth and Klich, Phys. Rev. Lett. 97, 160401 (2006). We study the convergence properties of the ... More

Quantum Polynomial FunctorsApr 05 2015May 20 2016We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this category (duality, ... More

Categorification and Heisenberg doubles arising from towers of algebrasSep 10 2013Sep 25 2014The Grothendieck groups of the categories of finitely generated modules and finitely generated projective modules over a tower of algebras can be endowed with (co)algebra structures that, in many cases of interest, give rise to a dual pair of Hopf algebras. ... More

Percolation in the Hyperbolic PlaneDec 30 1999Nov 09 2000This is a study of percolation in the hyperbolic plane and on regular tilings in the hyperbolic plane. The processes discussed include Bernoulli site and bond percolation on planar hyperbolic graphs, invariant dependent percolations on such graphs, and ... More

Polynomial representations and categorifications of Fock SpaceJan 12 2011Aug 29 2012The rings of symmetric polynomials form an inverse system whose limit, the ring of symmetric functions, is the model for the bosonic Fock space representation of the affine Lie algebra. We categorify this construction by considering an inverse limit of ... More

An elementary introduction to the geometry of quantum states with a picture bookJan 20 2019Feb 03 2019This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The space of states ... More

Seeing bulk topological properties of band insulators in small photonic latticesDec 24 2013We present a general scheme for measuring the bulk properties of non-interacting tight-binding models realized in arrays of coupled photonic cavities. Specifically, we propose to implement a single unit cell of the targeted model with tunable twisted ... More

The List-Decoding Size of Fourier-Sparse Boolean FunctionsApr 07 2015A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the number of ... More

Lack of Sphere Packing of Graphs via Non-Linear Potential TheoryOct 16 2009Nov 13 2010It is shown that there is no quasi-sphere packing of the lattice grid Z^{d+1} or a co-compact hyperbolic lattice of H^{d+1} or the 3-regular tree \times Z, in R^d, for all d. A similar result is proved for some other graphs too. Rather than using a direct ... More

A Planar Jitternig-Jets Pattern in Core-Collapse Supernova ExplosionsMar 20 2014Feb 24 2015We use 3D hydrodynamical numerical simulations and show that jittering bipolar jets that power core-collapse supernova (CCSN) explosions channel further accretion onto the newly born neutron star (NS) such that consecutive bipolar jets tend to be launched ... More

Fluctuations in the relaxation dynamics of mixed chaotic systemsOct 14 2012The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for this exponent. ... More

The contact conductance of a one-dimensional wire partly embedded in a superconductorSep 04 2007The conductance through a semi-infinite one-dimensional wire, partly embedded in a superconducting bulk electrode, is studied. When the electron-electron interactions within the wire are strongly repulsive, the wire effectively decouples from the superconductor. ... More

Enabling Cognitive Intelligence Queries in Relational Databases using Low-dimensional Word EmbeddingsMar 23 2016We apply distributed language embedding methods from Natural Language Processing to assign a vector to each database entity associated token (for example, a token may be a word occurring in a table row, or the name of a column). These vectors, of typical ... More

A Simple Isolation Criterion based on 3D Redshift Space MappingSep 22 2009We selected a sample of galaxies, extremely isolated in 3D redshift space, based on data from NED and the ongoing ALFALFA HI (21cm) survey. A simple selection criterion was employed: having no neighbors closer than 300 km/s in 3D redshift space. The environments ... More

Comments on Mesonic Correlators in the Worldline FormalismFeb 25 2011Jul 05 2011We elaborate on how to incorporate mesonic correlators into the worldline formalism. We consider possible applications to QCD-like theories in various dimensions. We focus on large-N_c two dimensional QCD (the 't Hooft model) and relate it to a single ... More

Rotating Accelerator-Mode IslandsDec 24 2006The existence of rotating accelerator-mode islands (RAIs), performing quasiregular motion in rotational resonances of order $m>1$ of the standard map, is firmly established by an accurate numerical analysis of all the known data. It is found that many ... More

Parametrically excited "Scars" in Bose-Einstein condensatesMar 05 2009May 12 2010Parametric excitation of a Bose-Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that when the condensate ... More

Solute Effects on the Helix-Coil TransitionJun 17 2002We discuss the effects of the solvent composition on the helix-coil transition of a polypeptide chain. We use a simple model to demonstrate that improving the hydrogen-bonding ability of the solvent can make the transition less cooperative, without affecting ... More

Entropy driven aggregation of adhesion sites of supported membranesJul 21 2010We study, by means of mean field calculations and Monte Carlo simulations of a lattice-gas model, the distribution of adhesion sites of a bilayer membrane and a supporting flat surface. Our model accounts for the many-body character of the attractive ... More

Formation of adhesion domains in stressed and confined membranesMar 23 2015The adhesion bonds connecting a lipid bilayer to an underlying surface may undergo a condensation transition resulting from an interplay between a short range attractive potential between them, and a long range fluctuation-induced potential of mean force. ... More

Non-deterministic branching programs with logarithmic repetition cannot efficiently compute small monotone CNFsApr 06 2016Apr 07 2016In this paper we establish an exponential lower bound on the size of syntactic non-deterministic read $d$-times branching programs for $d \leq \log n /10^5$ computing a class of monotone CNFs with a linear number of clauses. This result provides the first ... More

Uniform Infinite Planar TriangulationsJul 18 2002Mar 04 2003The existence of the weak limit as n --> infinity of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random triangulations ... More

Trees, not cubes: hypercontractivity, cosiness, and noise stabilityFeb 19 1999Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable.

The Aharonov Casher Effect: The Case of g not equal to 2Jun 28 2015The Aharonov Casher effect predicts the existence in two dimensions of ceil(Phi/2pi) -1 bounded zero modes associated with a magnetic flux Phi. Aharonov and Casher discussed the case of gyromagnetic factor equals 2, we will discuss the general case of ... More

Polynomial functors and categorifications of Fock space IINov 22 2011Aug 29 2012We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A affine Lie algebras. In the ... More

KPZ in one dimensional random geometry of multiplicative cascadesJun 08 2008We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables ... More

Recurrence of Distributional Limits of Finite Planar GraphsNov 02 2000Oct 27 2001Suppose that $G_j$ is a sequence of finite connected planar graphs, and in each $G_j$ a special vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a distributional limit $G$ of such graphs. Assume that the vertex degrees ... More

Basic properties of SLEJun 05 2001Jan 20 2004SLE is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed $\kappa$. This process is intimately connected with scaling limits of percolation clusters and with the outer boundary ... More

Pinched exponential volume growth implies an infinite dimensional isoperimetric inequalityMar 11 2003Let $G$ be a graph which satisfies $c^{-1} a^r \le |B(v,r)| \le c a^r$, for some constants $c,a>1$, every vertex $v$ and every radius $r$. We prove that this implies the isoperimetric inequality $|\partial A| \ge C |A| / \log(2+ |A|)$ for some constant ... More

Exploding Core-Collapse Supernovae by Jets-Driven Feedback MechanismJul 01 2013Nov 11 2013We study the flow structure in the jittering-jets explosion model of core-collapse supernovae (CCSNe) using 2.5D hydrodynamical simulations and find that some basic requirements for explosion are met by the flow. In the jittering-jets model jets are launched ... More

A Lattice Problem in Quantum NPJul 30 2003We consider coGapSVP_\sqrt{n}, a gap version of the shortest vector in a lattice problem. This problem is known to be in AM\cap coNP but is not known to be in NP or in MA. We prove that it lies inside QMA, the quantum analogue of NP. This is the first ... More

Effects of Edge Oxidation on the Structural, Electronic, and Magnetic Properties of Zigzag Boron Nitride NanoribbonsAug 08 2013The effects of edge chemistry on the relative stability and electronic properties of zigzag boron nitride nanoribbons (ZBNNRs) are investigated. Among all functional groups considered, fully hydroxylated ZBNNRs are found to be the most energetically stable. ... More

Lithium Mediated Benzene Adsorption on Graphene and Graphene NanoribbonsJun 10 2013The anchoring of benzene molecules on lithium adsorption sites at the surface of graphene and nanoribbons thereof are investigated. The effects of adsorbate densities, specific adsorption locations, and spin states on the structural stability and electronic ... More

Topological transitions in evaporating thin filmsJun 17 2012Jul 31 2012A thin water film evaporating from a cleaved mica substrate undergoes a first-order phase transition between two values of film thickness. During evaporation, the interface between the two phases develops a fingering instability similar to that observed ... More

Towards Strong Reverse Minkowski-type Inequalities for LatticesJun 22 2016We present a natural reverse Minkowski-type inequality for lattices, which gives upper bounds on the number of lattice points in a Euclidean ball in terms of sublattice determinants, and conjecture its optimal form. The conjecture exhibits a surprising ... More

Formation of dilute adhesion domains driven by weak elasticity-mediated interactionsJul 06 2016Cell-cell adhesion is established by specific binding of receptor and ligand proteins. The adhesion bonds attract each other and often aggregate into large clusters that are central to many biological processes. One possible origin of attractive interactions ... More

Muscle contraction and the elasticity-mediated crosstalk effectMay 09 2013Cooperative action of molecular motors is essential for many cellular processes. One possible regulator of motor coordination is the elasticity-mediated crosstalk (EMC) coupling between myosin II motors whose origin is the tensile stress that they collectively ... More

The Effect of Thermal Fluctuations on Schulman Area ElasticityJul 29 2003We study the elastic properties of a two-dimensional fluctuating surface whose area density is allowed to deviate from its optimal (Schulman) value. The behavior of such a surface is determined by an interplay between the area-dependent elastic energy, ... More

Novel Mechanisms for repulsive Casimir forcesDec 30 2008We present two novel models for repulsive Casimir interaction between positive perturbations. One example relies on non locality of the dielectric response and one relies on interference between (attractive) modes. Such examples are impossible to achieve ... More

Boundary proximity of SLENov 21 2007Dec 06 2007This paper examines how close the chordal $\SLE_\kappa$ curve gets to the real line asymptotically far away from its starting point. In particular, when $\kappa\in(0,4)$, it is shown that if $\beta>\beta_\kappa:=1/(8/\kappa-2)$, then the intersection ... More

A quantum analogue of Kostant's theorem for the general linear groupJul 01 2010A fundamental result in representation theory is Kostant's theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the general linear group, and from ... More

Tensor-based Hardness of the Shortest Vector Problem to within Almost Polynomial FactorsJun 11 2018$ \newcommand{\SVP}{\mathsf{SVP}} \newcommand{\NP}{\mathsf{NP}} \newcommand{\RTIME}{\mathsf{RTIME}} \newcommand{\RSUBEXP}{\mathsf{RSUBEXP}} \newcommand{\eps}{\epsilon} \newcommand{\poly}{\mathop{\mathrm{poly}}} $We show that unless $\NP \subseteq \RTIME ... More

Exploding Core-Collapse Supernovae with Jittering JetsMar 08 2011We argue that jittering jets, i.e., jets that have their launching direction rapidly change, launched by the newly formed neutron star in a core collapse supernova can explode the star. We show that under a wide range of parameters the fast narrow jets ... More