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Capillary-driven binding of thin triangular prisms at fluid interfacesFeb 08 2018We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $\mu m$, and the thickness of the prism is varied between 2 and 20 $\mu m$. For thickness ... More

Matrix models for 5d super Yang-MillsAug 09 2016Aug 14 2016In this contribution to the review on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S^5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point approximation. ... More

Plancherel Formulae associated to Filtrations of Nilpotent Lie GroupsDec 09 2012Dec 29 2012We study the conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable (relative discrete series) unitary representations, that fit together to form a filtration by normal subgroups. Then we use that filtration to ... More

Holographic three-point functions for short operatorsJun 14 2012Jul 25 2012We consider holographic three-point functions for operators dual to short string states at strong coupling in N=4 super Yang-Mills. We treat the states as point-like as they come in from the boundary but as strings in the interaction region in the bulk. ... More

Strong coupling from the Hubbard modelMar 22 2006Apr 03 2006It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, ... More

Circular Semiclassical String Solutions on AdS_5 x S_5Sep 05 2002May 16 2004We discuss two semiclassical string solutions on AdS_5\times S_5. In the first case, we consider a multiwrapped circular string pulsating in the radial direction of AdS_5, but fixed to a point on the S_5. We compute the energy of this motion as a function ... More

Quantum Corrections in p-adic String TheoryMay 30 2001We compute loop corrections in p-adic open string field theory. We argue that quantum effects induce a pole with m^2 ~ - ln g for the open string field at the locally stable vacuum. We also compute the one loop effective potential and show that the potential ... More

Mode Interactions of the Tachyon Condensate in p-adic String TheoryFeb 13 2001We study the fluctuation modes for lump solutions of the tachyon effective potential in p-adic open string theory. We find a discrete spectrum with equally spaced mass squared levels. We also find that the interactions derived from this field theory are ... More

Cycle Spaces of Infinite Dimensional Flag DomainsSep 10 2015Apr 23 2016Let $G$ be a complex simple direct limit group, specifically $SL(\infty;\mathbb{C})$, $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$. Let $\mathcal{F}$ be a (generalized) flag in $\mathbb{C}^\infty$. If $G$ is $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$ ... More

Infinite Dimensional Multiplicity Free Spaces I: Limits of Compact Commutative SpacesJan 25 2008We study direct limits $(G,K) = \varinjlim (G_n,K_n)$ of compact Gelfand pairs. First, we develop a criterion for a direct limit representation to be a multiplicity--free discrete direct sum of irreducible representations. Then we look at direct limits ... More

The SU(2) sector in AdS/CFTMar 18 2005Apr 24 2005In the large N limit of N=4 Super Yang-Mills, the mixing under dilatations of the SU(2) sector, single trace operators composed of L complex scalar fields of two types, is closed to all orders in perturbation theory. By relying on the AdS/CFT correspondence, ... More

Higher Loops Beyond the SU(2) SectorMay 26 2004Oct 10 2005We consider the case of coherent gauge invariant operators in the SU(3) and SO(4) sectors. We argue that in many cases, these sectors can be closed in the thermodynamic limit, even at higher loops. We then use a modification of the Bethe equations which ... More

Matrix Models and One Dimensional Open String Theory (Revised)Apr 06 1992Apr 10 1992We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls ... More

Infinite Dimensional Multiplicity Free Spaces II: Limits of Commutative NilmanifoldsJan 25 2008We study direct limits $(G,K) = \varinjlim (G_n,K_n)$ of Gelfand pairs of the form $G_n = N_n\rtimes K_n$ with $N_n$ nilpotent, in other words pairs $(G_n,K_n)$ for which $G_n/K_n$ is a commutative nilmanifold. First, we extend the criterion of \cite{W3} ... More

Complex Forms of Quaternionic Symmetric SpacesAug 28 2003Oct 02 2003This is a complete classification of the complex forms of quaternionic symmetric spaces

Stepwise Square Integrable Representations: the Concept and Some ConsequencesNov 29 2015There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on parabolic subgroups ... More

On the Analytic Structure of Commutative NilmanifoldsJul 01 2014In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases, the nilpotent ... More

The Plancherel Formula for Minimal Parabolic SubgroupsJun 27 2013Dec 18 2013In a recent paper we found conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable unitary representations that fit together to form a filtration by normal subgroups. That resulted in explicit character formulae, ... More

Stepwise Square Integrability for Nilradicals of Parabolic Subgroups and Maximal Amenable SubgroupsMay 20 2016In a series of recent papers we extended the notion of square integrability, for representations of nilpotent Lie groups, to that of stepwise square integrability. There we discussed a number of applications based on the fact that nilradicals of minimal ... More

Classical Analysis and Nilpotent Lie GroupsDec 06 2010Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I'll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifolds closely related to a nilpotent Lie group structure. There ... More

Solvability, Structure and Analysis for Minimal Parabolic SubgroupsOct 25 2016We examine the structure of the Levi component $MA$ in a minimal parabolic subgroup $P = MAN$ of a real reductive Lie group $G$, work out the cases where $M$ is commutative, verify that $P$ is solvable if and only if $M$ is commutative, and work out the ... More

Analytical Modeling of Galaxies at z>~6: Star Formation and Black Hole GrowthAug 03 2012Galaxies at z>~6 represent an important evolutionary link between the first galaxies and their modern counterparts. Modeling both the global and internal properties of these recently discovered objects can lead us to understand how they relate to even ... More

Matrix models for 5d super Yang-MillsAug 09 2016Oct 15 2016In this contribution to the review on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S^5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point approximation. ... More

Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-MillsDec 17 2010Jul 15 2011In this chapter of "Review of AdS/CFT Integrability" we introduce N=4 Super Yang-Mills. We discuss the global superalagebra PSU(2,2|4) and its action on gauge invariant operators. We then discuss the computation of the correlators of certain gauge invariant ... More

Rolling the tachyon in super BSFTMay 10 2002May 14 2002We investigate the rolling of the tachyon on the unstable D9 brane in Type IIA string theory by studying the BSFT action. The action is known for linear profiles of the tachyon, which is the expected asymptotic behavior of the tachyon as it approaches ... More

Stretched strings in tachyon condensation modelsMar 12 2002May 14 2002In this note, we consider the two derivative truncation of boundary string field theory for unstable D9 branes in Type IIA string theory. We construct multiples of the stable codimension 1 solitons that correspond to stacks of D8 branes. We find the fluctuation ... More

Asymptotic Freedom and Confinement from Type 0 String TheoryFeb 10 1999Feb 22 1999We argue that there are generic solutions to the type 0 gravity equations of motion that are confining in the infrared and have log scaling in the ultraviolet. The background curvature generically diverges in the IR. Nevertheless, there exist solutions ... More

Duality Symmetries for N=2 Supersymmetric QCD with Vanishing beta-FunctionsJun 30 1998Jul 07 1998We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation $(STS^{-1}T)^{2n+1}=1$. Thus, ... More

Homogeneity for a Class of Riemannian Quotient ManifoldsSep 19 2016We study riemannian coverings $\varphi: \widetilde{M} \to \Gamma\backslash \widetilde{M}$ where $\widetilde{M}$ is a normal homogeneous space $G/K_1$ fibered over another normal homogeneous space $M = G/K$ and $K$ is locally isomorphic to a nontrivial ... More

Principal series representations of infinite dimensional Lie groups, II: Construction of induced representationsAug 20 2012Oct 19 2012We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those parabolic subgroups ... More

Principal Series Representations of Infinite Dimensional Lie Groups, I: Minimal Parabolic SubgroupsApr 05 2012We study the structure of minimal parabolic subgroups of the classical infinite dimensional real simple Lie groups, corresponding to the classical simple direct limit Lie algebras. This depends on the recently developed structure of parabolic subgroups ... More

Confluent Hasse diagramsAug 26 2011Nov 13 2013We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with $O(n^2)$ features, in an $O(n) \times O(n)$ ... More

Relativistic Cyclotron Radiation Detection of Tritium Decay Electrons as a New Technique for Measuring the Neutrino MassApr 18 2009The shape of the beta decay energy distribution is sensitive to the mass of the electron neutrino. Attempts to measure the endpoint shape of tritium decay have so far seen no distortion from the zero-mass form, thus placing an upper limit of m_nu_beta ... More

Contractive multipliers from Hardy space to weighted Hardy spaceSep 17 2012It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\bbeta}$ can be factored as a fixed factor composed with the classical Schur multiplier (contractive multiplier between Hardy spaces). The result is applied ... More

Canonical transfer-function realization for Schur multipliers on the Drury-Arveson space and models for commuting row contractionsMar 07 2011We develop a $d$-variable analog of the two-component de Bran-ges-Rovnyak reproducing kernel Hilbert space associated with a Schur-class function on the unit disk. In this generalization, the unit disk is replaced by the unit ball in $d$-dimensional complex ... More

Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theoryMay 12 2014The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions, conservative ... More

Separating Vector Bundle Sections by Invariant MeansOct 19 2012We sharpen the construction of representation space in the paper "Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations". We show that the principal series representation spaces constructed there, ... More

Event Rate and Einstein Time Evaluation in Pixel MicrolensingJan 29 1999It has been shown that a flux--weighted full width at half maximum timescale of a microlensing event can be used in an unbiased estimator of the optical depth. For the first time, this allows a physical parameter to be easily estimated from pixel microlensing ... More

On the Secular Behavior of Irregular SatellitesAug 05 2004Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because ... More

An N=2 Superconformal Fixed Point with E_6 Global SymmetryAug 08 1996We obtain the elliptic curve corresponding to an $N=2$ superconformal field theory which has an $E_6$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. We also find the Seiberg-Witten differential $\lambda_{SW}$ for this theory. This differential ... More

Phases of planar 5-dimensional supersymmetric Chern-Simons theoryAug 12 2014Feb 25 2015In this paper we investigate the large-$N$ behavior of 5-dimensional $\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour ... More

Superconformal Fixed Points with E_n Global SymmetryOct 10 1996We obtain the elliptic curve and the Seiberg-Witten differential for an $N=2$ superconformal field theory which has an $E_8$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. The differential has 120 poles corresponding to half the charged ... More

Verifying the Identity of High-Redshift Massive Galaxies Through the Clustering of Lower Mass Galaxies Around ThemNov 03 2007Jul 13 2008Massive high-redshift galaxies form in over-dense regions where the probability of forming other galaxies is also strongly enhanced. Given an observed flux of a galaxy, the inferred mass of its host halo tends to be larger as its inferred redshift increases. ... More

The bitangential matrix Nevanlinna-Pick interpolation problem revisitedNov 21 2016We revisit four approaches to the BiTangential Operator Argument Nevanlinna-Pick (BTOA-NP) interpolation theorem on the right half plane: (1) the state-space approach of Ball-Gohberg-Rodman, (2) the Fundamental Matrix Inequality approach of the Potapov ... More

Gauge theories with 16 supersymmetries on spheresFeb 25 2015Aug 14 2016We give a unified approach to localization of maximally symmetric gauge theories on spheres, including $S^6$ and $S^7$. The approach follows Pestun's method of dimensionally reducing from 10 dimensional super Yang-Mills. The resulting theories have a ... More

Hyperelliptic curves for Supersymmetric Yang-MillsJul 06 1995In this paper we discuss the hyperelliptic curve for $N=2$ $SU(3)$ super Yang-Mills with six flavors of hypermultiplets. We start with a generic genus two surface and construct the curve in terms of genus two theta functions. From this one can construct ... More

Constraining the Minimum Mass of High-Redshift Galaxies and Their Contribution to the Ionization State of the IGMOct 11 2010We model the latest HST WFPC3/IR observations of > 100 galaxies at redshifts z=7-8 in terms of a hierarchical galaxy formation model with starburst activity. Our model provides a distribution of UV luminosities per dark matter halo of a given mass and ... More

Sp(2)/U(1) and a Positive Curvature ProblemFeb 10 2015Mar 10 2015A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ ... More

Weighted Bergman spaces: shift-invariant subspaces and input/state/output linear systemsSep 17 2012It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the ... More

de Branges-Rovnyak spaces and norm-constraint interpolationMay 12 2014For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$. A companion survey provides equivalent definitions and basic properties of ... More

The inverse commutant lifting problem: characterization of associated Redheffer linear-fractional mapsApr 03 2010It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal unitary extensions ... More

Locally symmetric homogeneous Finsler spacesJun 16 2012Let $(M,F)$ be a connected Finsler space and $d$ the distance function of $(M,F)$. A Clifford translation is an isometry $\rho$ of $(M,F)$ of constant displacement, in other words such that $d(x,\rho(x))$ is a constant function on $M$. In this paper we ... More

Killing Vector Fields of Constant Length on Riemannian Normal Homogeneous SpacesDec 10 2014Apr 06 2016Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group manifolds or, more ... More

Extension of Symmetric Spaces and Restriction of Weyl Groups and Invariant PolynomialsDec 02 2010Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion that ensure ... More

Geometry of the Borel -- de Siebenthal Discrete SeriesJan 28 2009Let $G_0$ be a connected, simply connected real simple Lie group. Suppose that $G_0$ has a compact Cartan subgroup $T_0$, so it has discrete series representations. Relative to $T_0$ there is a distinguished positive root system $\Delta^+$ for which there ... More

Zero-pole interpolation for matrix meromorphic functions on a compact Riemann surface, and a matrix Fay trisecant identityDec 23 1997Feb 08 1999This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e., having prescribed zeros and poles with directional as well as multiplicity information ... More

Approximating Minimum-Cost k-Node Connected Subgraphs via Independence-Free GraphsDec 17 2012We present a 6-approximation algorithm for the minimum-cost $k$-node connected spanning subgraph problem, assuming that the number of nodes is at least $k^3(k-1)+k$. We apply a combinatorial preprocessing, based on the Frank-Tardos algorithm for $k$-outconnectivity, ... More

$N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$Jan 12 1996Feb 01 1996We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular, uniqueness arguments ... More

Cycle Space Constructions for Exhaustions of Flag DomainsJul 13 2008In the study of complex flag manifolds, flag domains and their cycle spaces, a key point is the fact that the cycle space $\mathcal M_D$ of a flag domain $D$ is a Stein manifold. That fact has a long history. The earliest approach relied on construction ... More

Light-Cone Distortion of the Clustering and Abundance of Massive Galaxies at High-RedshiftsNov 15 2007Mar 13 2008Observational surveys of galaxies are not trivially related to single-epoch snapshots from computer simulations. Observationally, an increase in the distance along the line-of-sight corresponds to an earlier cosmic time at which the properties of the ... More

Can the excess in the FeXXVI Ly gamma line from the Galactic Center provide evidence for 17 keV sterile neutrinos?Jan 01 2010The standard model of particle physics assumes that neutrinos are massless, although adding non-zeros is required by the experimentally established phenomenon of neutrino oscillations requires neutrinos to have non-zero mass. Sterile neutrinos (or right-handed ... More

Interpolation in the noncommutative Schur-Agler classJun 26 2005The class of Schur-Agler functions over a domain ${\mathcal D} \subset {\mathbb C}^{d}$ is defined as the class of holomorphic operator-valued functions on ${\mathcal D}$ for which a certain von Neumann inequality is satisfied when a commuting tuple of ... More

de Branges-Rovnyak spaces: basics and theoryMay 12 2014For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic ... More

Pseudo-Riemannian Weakly Symmetric ManifoldsJul 22 2011There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics ... More

Three-point correlators from string amplitudes: Mixing and Regge spinsOct 17 2014Jan 20 2016This paper has two parts. We first compute the leading contribution to the strong-coupling mixing between the Konishi operator and a double-trace operator composed of chiral primaries by using flat-space vertex operators for the string-duals of the operators. ... More

Semisimple Weakly Symmetric Pseudo--Riemannian ManifoldsJul 04 2017Jan 10 2018We develop the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derive the classification from the cases where $G$ is compact, and then we discuss the (isotropy) ... More

Acoustic Cyclotron Resonance and Giant High Frequency Magnetoacoustic Oscillations in Metals with Locally Flattened Fermi SurfaceNov 26 1999Jun 30 2005We consider the effect of local flattening on the Fermi surface (FS) of a metal upon geometric oscillations of the velocity and attenuation of ultrasonic waves in the neighborhood of the acoustic cyclotron resonance. It is shown that such peculiarities ... More

Deconfinement and Dissipation in Quantum Hall "Josephson" TunnelingJan 09 2003Jul 31 2003The zero-bias tunneling resonance in quantum Hall bilayer systems is investigated via numerical simulations of the classical two dimensional XY model with a symmetry-breaking field. Disorder is included in the model, and is shown to nucleate strings of ... More

Quantum protocols for anonymous voting and surveyingApr 21 2005Jun 04 2007We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the ... More

The Canonical Perfect Bose Gas in Casimir BoxesMay 14 2004We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the ... More

Images of HCO+ (1-0) Emission in a Molecular Cloud near 1E1740.7-2942Nov 09 1994Nov 10 1994We have observed the hard X-ray source 1E1740.7-2942 in the HCO+ (1-0) line using the Owens Valley millimeter interferometer. Previous single dish observations have found HCO+ emission coincident with the location of the radio continuum hot spots of the ... More

Object-image correspondence for curves under projectionsFeb 06 2012Mar 15 2013We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of setting up a system ... More

Ionization Sources and Physical Conditions in the Diffuse Ionized Gas Halos of Four Edge-On GalaxiesNov 29 2000Dec 01 2000Deep long-slit spectra of the diffuse ionized gas halos of the edge-on spiral galaxies NGC 4302 and UGC 10288 are presented. These data, along with previously presented data for NGC 5775 and NGC 891, are used to address the issue of how DIG halos are ... More

Modelling the angle-dependent magnetoresistance oscillations of Fermi surfaces with hexagonal symmetryJun 03 2016By solving the Boltzmann transport equation we investigate theoretically the general form of oscillations in the resistivity caused by varying the direction of an applied magnetic field for the case of quasi-two dimensional systems on hexagonal lattices. ... More

Rational Cayley inner Herglotz-Agler functions: positive-kernel decompositions and transfer-function realizationsOct 03 2013The Bessmertny\u{\i} class consists of rational matrix-valued functions of $d$ complex variables representable as the Schur complement of a block of a linear pencil $A(z)=z_1A_1+\cdots+z_dA_d$ whose coefficients $A_k$ are positive semidefinite matrices. ... More

Transfer-function realization for multipliers of the Arveson spaceOct 20 2006An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers for the reproducing kernel Hilbert space ${\mathcal H}(k_{d})$ on the unit ball ${\mathbb B}^{d} \subset {\mathbb ... More

Multivariable backward-shift-invariant subspaces and observability operatorsOct 20 2006It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the ... More

Exponentially Localized Magnetic Fields for Single-Spin Quantum Logic GatesOct 15 2003Feb 03 2004An infinite array of parallel current-carrying wires is known, from the field of neutral particle optics, to produce an exponentially localized magnetic field when the current direction is antiparallel in adjacent wires. We show that a finite array of ... More

Density Correlation Functions in Calogero Sutherland ModelsMay 01 1994May 04 1994Using arguments from two dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density correlation function for coupling $l$ and $1/l$, where $l$ is an integer. We present ... More

Tunneling and delocalization in hydrogen bonded systems: a study in position and momentum spaceApr 29 2009Novel experimental and computational studies have uncovered the proton momentum distribution in hydrogen bonded systems. In this work, we utilize recently developed open path integral Car-Parrinello molecular dynamics methodology in order to study the ... More

Direct Systems of Spherical Functions and RepresentationsOct 04 2011Nov 09 2012Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces ... More

Branching of Representations to Symmetric SubgroupsDec 03 2008Sep 24 2009Let $\gg$ be the Lie algebra of a compact Lie group and let $\theta$ be any automorphism of $\gg$. Let $\gk$ denote the fixed point subalgebra $\gg^\theta$. In this paper we present LiE programs that, for any finite dimensional complex representation ... More

Test functions, Schur-Agler classes and transfer-function realizations: the matrix-valued settingSep 17 2011Given a collection of test functions, one defines the associated Schur-Agler class as the intersection of the contractive multipliers over the collection of all positive kernels for which each test function is a contractive multiplier. We indicate extensions ... More

Extension of the $ν$-metricFeb 27 2010We extend the $\nu$-metric introduced by Vinnicombe in robust control theory for rational plants to the case of infinite-dimensional systems/classes of nonrational transfer functions.

Schur-class multipliers on the Arveson space: de Branges-Rovnyak reproducing kernel spaces and commutative transfer-function realizationsOct 20 2006An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers $S$ for the reproducing kernel Hilbert space ${\mathcal H}(k_{d})$ on the unit ball ${\mathbb B}^{d} \subset {\mathbb ... More

Convexity analysis and matrix-valued Schur class over finitely connected planar domainsSep 17 2011We identify the set of extreme points and apply Choquet theory to a normalized matrix-measure ball subject to finitely many linear side constraints. As an application we obtain integral representation formulas for the Herglotz class of matrix-valued functions ... More

Ion Transport and Precipitation Kinetics as Key Aspects of Stress Generation on Pore Walls Induced by Salt CrystallizationFeb 06 2018The stress generation on pore walls due to the growth of a sodium chloride crystal in a confined aqueous solution is studied from evaporation experiments in microfluidic channels in conjunction with numerical computations of crystal growth. The study ... More

Implications of SU(2) symmetry on the dynamics of population difference in the two-component atomic vaporAug 17 2000Nov 03 2000We present an exact many body solution for the dynamics of the population difference $N_2-N_1$ induced by an rf-field in the two-component atomic cloud characterized by equal scattering lengths. This situation is very close to the actual JILA experiments ... More

Object-image correspondence for curves under finite and affine camerasApr 02 2010Feb 28 2011We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain modification of the equivalence ... More

Faint AGN in z>~6 Lyman-break Galaxies Powered by Cold Accretion and Rapid Angular Momentum TransportJan 05 2012Aug 03 2012We develop a radiation pressure-balanced model for the interstellar medium of high-redshift galaxies that describes many facets of galaxy formation at z>~6, including star formation rates and distributions and gas accretion onto central black holes. We ... More

Interacting Fermion Systems from Two Dimensional QCDSep 08 1993We consider two dimensional U(N) QCD on the cylinder with a timelike Wilson line in an arbitrary representation. We show that the theory is equivalent to N fermions with internal degrees of freedom which interact among themselves with a generalized Sutherland-type ... More

Equivalence of Two Dimensional QCD and the $c=1$ Matrix ModelMar 27 1993We consider two dimensional QCD with the spatial dimension compactified to a circle. We show that the states in the theory consist of interacting strings that wind around the circle and derive the Hamiltonian for this theory in the large $N$ limit, complete ... More

A Framework for Empirical Galaxy Phenomenology: The Scatter in Galaxy Ages and Stellar MetallicitiesApr 07 2014Jan 28 2015We develop a theoretical framework that extracts a deeper understanding of galaxy formation from empirically-derived relations among galaxy properties by extending the main-sequence integration method for computing galaxy star formation histories. We ... More

The $a$-theorem and the Asymptotics of 4D Quantum Field TheoryApr 23 2012Nov 09 2012We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group ... More

Injectivity of the Double Fibration Transform for Cycle Spaces of Flag DomainsAug 29 2003The basic setup consists of a complex flag manifold $Z=G/Q$ where $G$ is a complex semisimple Lie group and $Q$ is a parabolic subgroup, an open orbit $D = G_0(z) \subset Z$ where $G_0$ is a real form of $G$, and a $G_0$--homogeneous holomorphic vector ... More

Multiple-scale analysis on the radiation within the coupled KdV equationsSep 30 2016A multiple scale model of the nonlinearly coupled KdV equations is established to predict mechanism of interaction of equatorial Rossby waves and barotropic waves in certain case. Analytically, predicted precursor radiation is a centrosymmetric object ... More

Noncommutative reproducing kernel Hilbert spacesFeb 02 2016The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and operator theory. ... More

Interpolation and transfer-function realization for the noncommutative Schur-Agler classFeb 02 2016The Schur-Agler class consists of functions over a domain satisfying an appropriate von Neumann inequality. Originally defined over the polydisk, the idea has been extended to general domains in multivariable complex Euclidean space with matrix polynomial ... More

Extension of the $ν$-metric: the $H^\infty$ caseOct 09 2010An abtract $\nu$-metric was introduced by Ball and Sasane, with a view towards extending the classical $\nu$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional ... More

Linearized force constants method for lattice dynamics in mixed semiconductorsSep 19 2007A simple and accurate method of calculating phonon spectra in mixed semiconductors alloys, on the basis of preliminarily (from first principles) relaxed atomic structure, is proposed and tested for (Zn,Be)Se and (Ga,In)As solid solutions. The method uses ... More