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Optical decoherence and spectral diffusion in an erbium-doped silica glass fiber featuring long-lived spin sublevelsSep 23 2016Nov 21 2016Understanding decoherence in cryogenically-cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly ... More

Optical decoherence and spectral diffusion in an erbium-doped silica glass fiber featuring long-lived spin sublevelsSep 23 2016Understanding decoherence in cryogenically-cooled rare-earth-ion doped glass fibers is of fundamental interest and a prerequisite for applications of these material in quantum information applications. Here we study the coherence properties in a weakly ... More

Quadratic Zeeman effect and spin-lattice relaxation of Tm$^{3+}$:YAG at high magnetic fieldsAug 22 2016Anisotropy of the quadratic Zeeman effect for the $^3{\rm H}_6 \rightarrow \, ^3{\rm H}_4$ transition at 793 nm wavelength in $^{169}$Tm$^{3+}$-doped Y$_3$Al$_5$O$_{12}$ is studied, revealing shifts ranging from near zero up to + 4.69 GHz/T$^2$ for ions ... More

Modification of phonon processes in nanostructured rare-earth-ion-doped crystalsApr 09 2015Jun 27 2016Nano-structuring impurity-doped crystals affects the phonon density of states and thereby modifies the atomic dynamics induced by interaction with phonons. We propose the use of nano-structured materials in the form of powders or phononic bandgap crystals ... More

Electron Spin Coherences in Rare-Earth Optically Excited States for Microwave to Optical Quantum TransducersFeb 09 2018Feb 16 2018Efficient and reversible optical to microwave coherent transducers are required to enable entanglement transfer between superconducting qubits and light for quantum networks. Rare-earth-doped crystals that possess narrow optical and spin transitions are ... More

Effects of fabrication methods on spin relaxation and crystallite quality in Tm-doped Y$_2$Al$_5$O$_{12}$ powders studied using spectral hole burningSep 25 2015Apr 27 2016High-quality rare-earth-ion (REI) doped materials are a prerequisite for many applications such as quantum memories, ultra-high-resolution optical spectrum analyzers and information processing. Compared to bulk materials, REI doped powders offer low-cost ... More

Electron Spin Coherences in Rare-Earth Optically Excited States for Microwave to Optical Quantum TransducersFeb 09 2018Efficient and reversible optical to microwave coherent transducers are required to enable entanglement transfer between superconducting qubits and light for quantum networks. Rare-earth-doped crystals that possess narrow optical and spin transitions are ... More

Efficient and long-lived Zeeman-sublevel atomic population storage in an erbium-doped glass fiberJul 10 2015Jan 08 2016Long-lived population storage in optically pumped levels of rare-earth ions doped into solids, referred to as persistent spectral hole burning, is of significant fundamental and technological interest. However, the demonstration of deep and persistent ... More

Modification of relaxation dynamics in Tb$^{3+}$:Y$_3$Al$_5$O$_{12}$ nanopowdersNov 07 2017Mar 01 2018Nanostructured rare-earth-ion doped materials are increasingly being investigated for on-chip implementations of quantum information processing protocols as well as commercial applications such as fluorescent lighting. However, achieving high-quality ... More

Effects of mechanical processing and annealing on optical coherence properties of Er$^{3+}$:LiNbO$_3$ powdersJan 20 2017Optical coherence lifetimes and decoherence processes in erbium-doped lithium niobate (Er$^{3+}$:LiNbO$_3$) crystalline powders are investigated for materials that underwent different mechanical and thermal treatments. Several complimentary methods are ... More

Characterization of ${}^{171}Yb^{3+}\!:\! YVO_4$ for photonic quantum technologiesMay 03 2018Rare-earth ions in crystals are a proven solid-state platform for quantum technologies in the ensemble regime and attractive for new opportunities at the single ion level. Among the trivalent rare earths, ${}^{171}\mathrm{Yb}^{3+}$ is unique in that it ... More

A characterization of semiprojectivity for commutative C*-algebrasJan 10 2011Jan 26 2011Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, ... More

Semiprojectivity with and without a group actionMar 13 2014The equivariant version of semiprojectivity was recently introduced by the first author. We study properties of this notion, in particular its relation to ordinary semiprojectivity of the crossed product and of the algebra itself. We show that equivariant ... More

The Mixmaster cosmological metricsMay 27 1994This paper begins with a short presentation of the Bianchi IX or ``Mixmaster'' cosmological model, and some ways of writing the Einstein equations for it. There is then an interlude describing how I came to a study of this model, and then a report of ... More

Spherical Harmonic Decomposition on a Cubic GridOct 12 1999A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment ... More

Precis of General RelativityAug 18 1995Omitting the motivations and historical connections, and also the detailed calculations, I state succinctly the principles that determine the relativistic idealization of a GPS system. These determine the results that Ashby presents in his tutorial.

Yilmaz Cancels NewtonApr 28 1995Apr 28 1995A central tenet of the new theory of gravity proposed by H. Yilmaz is the inclusion of a gravitational stress-energy tensor $-{t_\mu}^\nu$ along with the matter stress-energy tensor ${T_\mu}^\nu$ on the right hand side of the Einstein field equations. ... More

Closed-form solutions of the Schroedinger equation for a class of smoothed Coulomb potentialsApr 15 1997An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular momentum $l$.

Intergalactic Baryons in the Local UniverseDec 02 2008Simulations predict that shocks from large-scale structure formation and galactic winds have reduced the fraction of baryons in the warm, photoionized phase (the Lya forest) from nearly 100% in the early universe to less than 50% today. Some of the remaining ... More

Over the Rainbow: Numerical Relativity beyond Scri+Dec 30 2005Mar 13 2006This is a study of the behavior of wave equations in conformally compactified spacetimes suited to the use of computational boundaries beyond Scri+. There light cones may be adjusted for computational convenience and/or Scri+ may be approximated by a ... More

Hyperboloidal Slices and Artificial Cosmology for Numerical RelativitySep 20 2004Mar 11 2006This preliminary report proposes integrating the Maxwell equations in Minkowski spacetime using coordinates where the spacelike surfaces are hyperboloids asymptotic to null cones at spatial infinity. The space coordinates are chosen so that Scri+ occurs ... More

The inversion number and the major index are asymptotically jointly normally distributed on wordsFeb 27 2013In a recent paper, Baxter and Zeilberger show that the two most important Mahonian statistics, the inversion number and the major index, are asymptotically independently normally distributed on permutations. In another recent paper, Canfield, Janson and ... More

A counter-example to Martino's conjecture about generic Calogero-Moser familiesJan 21 2013Sep 25 2013The Calogero-Moser families are partitions of the irreducible characters of a complex reflection group derived from the block structure of the corresponding restricted rational Cherednik algebra. It was conjectured by Martino in 2009 that the generic ... More

The topological dimension of type I C*-algebrasOct 16 2012Feb 05 2013While there is only one natural dimension concept for separable, metric spaces, the theory of dimension in noncommutative topology ramifies into different important concepts. To accommodate this, we introduce the abstract notion of a noncommutative dimension ... More

Inductive limits of projective C*-algebrasMay 10 2011Dec 14 2017We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an inductive limit of ... More

The generator rank for C*-algebrasOct 24 2012The invariant that assigns to a C*-algebra its minimal number of generators lacks natural permanence properties. In particular, it may increase when passing to ideals or inductive limits. It is therefore hard to compute this invariant directly. To obtain ... More

Inductive limits of semiprojective C*-algebrasApr 13 2018Feb 18 2019We prove closure properties for the class of C*-algebras that are inductive limits of semiprojective C*-algebras. Most importantly, we show that this class is closed under shape domination, and so in particular under shape and homotopy equivalence. It ... More

Preduals for spaces of operators involving Hilbert spaces and trace-class operatorsMar 03 2017Mar 27 2018Continuing the study of preduals of spaces $\mathcal{L}(H,Y)$ of bounded, linear maps, we consider the situation that $H$ is a Hilbert space. We establish a natural correspondence between isometric preduals of $\mathcal{L}(H,Y)$ and isometric preduals ... More

Restricted rational Cherednik algebrasMar 16 2016We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at t=0. Their representation theory is connected to the geometry of the Calogero-Moser ... More

The number of roots of full supportFeb 26 2016Chapoton has observed a simple product formula for the number of reflections in a finite Coxeter group that have full support. We give a uniform proof of his formula for Weyl groups.

Inductive limits of projective C*-algebrasMay 10 2011We show that a C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, i.e., is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an inductive limit of projectives, and one ... More

On the H-triangle of generalised nonnesting partitionsMay 02 2013Oct 31 2013To a crystallographic root system \Phi, and a positive integer k, there are associated two Fuss-Catalan objects, the set of nonnesting partitions NN^(k)(\Phi), and the cluster complex \Delta^(k)(\Phi). These posess a number of enumerative coincidences, ... More

Semiprojectivity and semiinjectivity in different categoriesFeb 14 2018Projectivity and injectivity are fundamental notions in category theory. We consider natural weakenings termed semiprojectivity and semiinjectivity, and study these concepts in different categories. For example, in the category of metric spaces, (semi)injective ... More

The number of roots of full supportFeb 26 2016Jan 30 2017Chapoton has observed a simple product formula for the number of reflections in a finite Coxeter group that have full support. We give a uniform proof of his formula for Weyl groups. We furthermore refine his formula by the length of the roots.

CHAMP: A Cherednik Algebra Magma PackageMar 26 2014Jan 20 2015We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general Las Vegas algorithm ... More

Blocks in flat families of finite-dimensional algebrasOct 21 2015Dec 06 2017We study the behavior of blocks in flat families of finite-dimensional algebras. In a general setting we construct a finite directed graph encoding a stratification of the base scheme according to the block structures of the fibers. This graph can be ... More

A new cyclic sieving phenomenon for Catalan objectsJan 15 2016Feb 25 2016Based on computational experiments, Jim Propp and Vic Reiner suspected that there might exist a sequence of combinatorial objects $X_n$, each carrying a natural action of the cyclic group $C_{n-1}$ of order $n-1$ such that the triple $\left(X_n,C_{n-1},\frac{1}{[n+1]_q}{2n ... More

Decomposition matrices are generically trivialFeb 20 2014Jun 15 2015We establish a genericity property in the representation theory of a flat family of finite-dimensional algebras in the sense of Cline-Parshal-Scott. More precisely, we show that the decomposition matrices as introduced by Geck and Rouquier of an algebra ... More

From Anderson to ZetaApr 28 2015Jul 15 2016For an irreducible crystallographic root system $\Phi$ and a positive integer $p$ relatively prime to the Coxeter number $h$ of $\Phi$, we give a natural bijection $\mathcal{A}$ from the set $\widetilde{W}^p$ of affine Weyl group elements with no inversions ... More

Mackey functors and abelian class field theoriesNov 03 2011Motivated by the work of J\"urgen Neukirch and Ivan Fesenko we propose a general definition of an abelian class field theory from a purely group-theoretical and functorial point of view. This definition allows a modeling of abelian extensions of a field ... More

Adelic Geometry and PolarityNov 17 2011In the present paper we generalise transference theorems from the classical geometry of numbers to the geometry of numbers over the ring of adeles of a number field. To this end we introduce a notion of polarity for adelic convex bodies.

Blocks in flat families of finite-dimensional algebrasOct 21 2015Aug 25 2016We study the behavior of blocks in flat families of finite-dimensional algebras. In a general setting we construct a finite directed graph encoding a stratification of the base scheme according to the block structures of the fibers. We furthermore show ... More

On floors and ceilings of the k-Catalan arrangementNov 22 2013Nov 05 2014The set of dominant regions of the $k$-Catalan arrangement of a crystallographic root system $\Phi$ is a well-studied object enumerated by the Fu{\ss}-Catalan number $Cat^{(k)}(\Phi)$. It is natural to refine this enumeration by considering floors and ... More

On three-dimensional dilational elastic metamaterialsOct 11 2013Dilational materials are stable three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and characterize crystalline metamaterials approaching this ideal. To reveal all modes, we calculate the phonon ... More

Some Remarks on Kite Pseudo Effect AlgebrasAug 26 2013Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group $G$, a set $I$ and with two bijections $\lambda,\rho:I \to I.$ Using a clever construction on the ordinal sum of ... More

High-density nuclear matter with nonlocal confining solitonsJul 30 1997An infinite system of nonlocal, individually confining solitons is considered as a model of high-density nuclear matter. The soliton-lattice problem is discussed in the Wigner-Seitz approximation. The cell size is varied to study the density dependence ... More

Effective one-component description of two-component Bose-Einstein condensate dynamicsOct 29 2004We investigate dynamics in two-component Bose-Einstein condensates in the context of coupled Gross-Pitaevskii equations and derive results for the evolution of the total density fluctuations. Using these results, we show how, in many cases of interest, ... More

Black Holes with Weyl Charge and Non-Riemannian WavesSep 06 1995A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations ... More

The conjugacy problem and related problems in lattice-ordered groupsJul 04 2005May 17 2007We study, from a constructive computational point of view, the techniques used to solve the conjugacy problem in the "generic" lattice-ordered group Aut(R) of order automorphisms of the real line. We use these techniques in order to show that for each ... More

Relativistic Scalar Gravity: A Laboratory for Numerical RelativityOct 10 1999We present here a relativistic theory of gravity in which the spacetime metric is derived from a single scalar field $\Phi$. The field equation, derived from a simple variational principle, is a non-linear flat-space four-dimensional wave equation which ... More

Loewy lengths of blocks with abelian defect groupsJul 29 2016We consider $p$-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index $p$. Using this, we show that if $B$ is a $2$-block of a finite group with abelian defect ... More

Saturation Properties of Nuclear Matter with a Nonlocal Confining SolitonsAug 26 1998We examine saturation properties of a quark-based picture of nuclear matter. Soliton matter consisting of nonlocal confining solitons is used to model nuclear matter. Each composite nucleon is described by a non-topological soliton as given by the Global ... More

Implementing Majorana fermions in a cold-atom honeycomb lattice with textured pairingsFeb 24 2018Aug 25 2018Recent studies in the realization of Majorana fermion (MF) quasiparticles have focused on engineering topological superconductivity by combining conventional superconductors and spin-textured electronic materials. We propose an effective model to create ... More

Heavily Damped Motion of One-Dimensional Bose Gases in an Optical LatticeJul 18 2008Feb 01 2009We study the dynamics of strongly correlated one-dimensional Bose gases in a combined harmonic and optical lattice potential subjected to sudden displacement of the confining potential. Using the time-evolving block decimation method, we perform a first-principles ... More

Current-Voltage Curves for Molecular Junctions Computed Using All-Electron Basis SetsSep 19 2006We present current-voltage (I-V) curves computed using all-electron basis sets on the conducting molecule. The all-electron results are very similar to previous results obtained using effective core potentials (ECP). A hybrid integration scheme is used ... More

Current-voltage curves for molecular junctions: the effect of substituentsJun 28 2007We present current-voltage (I-V) curves for phenylene ethynylene oligomers between two Au surfaces computed using a Density Functional Theory/Green's Function approach. In addition to the parent molecule, two different substituents are considered: one ... More

Transport in Molecular Junctions with Different Metallic ContactsSep 19 2006Ab initio calculations of phenyl dithiol connected to Au, Ag, Pd, and Pt electrodes are performed using non-equilibrium Green's functions and density functional theory. For each metal, the properties of the molecular junction are considered both in equilibrium ... More

Fast Frontend Electronics for high luminosity particle detectorsFeb 17 2015Future experiments of nuclear and particle physics are moving towards the high luminosity regime, in order to access suppressed processes like rare B decays or exotic charmonium resonances. In this scenario, high rate capability is a key requirement for ... More

Tm$^{3+}$:Y$_3$Ga$_5$O$_{12}$ materials for spectrally multiplexed quantum memoriesAug 08 2014Oct 22 2014We investigate the relevant spectroscopic properties of the 795 nm $^3$H$_6$$\leftrightarrow$$^3$H$_4$ transition in 1% Tm$^{3+}$:Y$_3$Ga$_5$O$_{12}$ at temperatures as low as 1.2 K for optical quantum memories based on persistent spectral tailoring of ... More

Optical decoherence studies of Tm$^{3+}$:Y$_3$Ga$_5$O$_{12}$Oct 22 2014Decoherence of the 795 nm $^3$H$_6$ to $^3$H$_4$ transition in 1%Tm$^{3+}$:Y$_3$Ga$_5$O$_{12}$ (Tm:YGG) is studied at temperatures as low as 1.2 K. The temperature, magnetic field, frequency, and time-scale (spectral diffusion) dependence of the optical ... More

Banach algebras generated by an invertible isometry of an $L^p$-spaceMay 22 2014Dec 18 2014We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the commutative ... More

Virtual braid groups of type B and weak categorificationDec 18 2009Mar 17 2011We define virtual braid groups of type B and construct a morphism from such a group to the group of isomorphism classes of some invertible complexes of bimodules up to homotopy.

Restricted Successive MinimaFeb 06 2013Mar 13 2013We give bounds on the successive minima of an $o$-symmetric convex body under the restriction that the lattice points realizing the successive minima are not contained in a collection of forbidden sublattices. Our investigations extend former results ... More

Representations of $p$-convolution algebras on $L^q$-spacesSep 27 2016For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are operator algebras ... More

Note on adelic triangulations and an Adelic Blichfeldt-type inequalityMay 22 2014We introduce a notion of convex hull and polytope into adele space. This allows to consider adelic triangulations which, in particular, lead to an adelic blichfeldt-type inequality, complementing former results.

Functoriality of group algebras acting on $L^p$-spacesAug 24 2014We continue our study of group algebras acting on $L^p$-spaces, particularly of algebras of $p$-pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that $p$-pseudofunctions are functorial with ... More

Quotients of Banach algebras acting on $L^p$-spacesDec 12 2014Mar 29 2016We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\neq 2$, is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our earlier study ... More

Cuspidal Calogero-Moser and Lusztig families for Coxeter groupsMay 03 2015Jun 13 2016The goal of this paper is to compute the cuspidal Calogero-Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by first computing the symplectic leaves of the associated Calogero-Moser space and then by classifying ... More

Type C parking functions and a zeta mapNov 14 2014We introduce type C parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type C parking functions to regions of the Shi arrangement of type C, encoded as diagonally labelled ballot ... More

Strange ExpectationsAug 21 2015Let gcd(a,b)=1. J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a,b)-core is (a^2-1)(b^2-1)/24, and that this maximum was achieved by a unique core. P. Johnson combined Ehrhart theory with the polynomial method to prove ... More

Isomorphisms of Algebras of Convolution OperatorsSep 05 2018Oct 02 2018For $p,q\in [1,\infty)$, we study the isomorphism problem for the $p$- and $q$-convolution algebras associated to locally compact groups. While it is well known that not every group can be recovered from its group von Neumann algebra, we show that this ... More

How much information about a dynamical system do its recurrences contain?Jun 27 2007Jul 04 2007We show that, under suitable assumptions, Poincare recurrences of a dynamical system determine its topology in phase space. Therefore, dynamical systems with the same recurrences are topologically equivalent.

Preduals and complementation of spaces of bounded linear operatorsSep 17 2016For Banach spaces X and Y, we establish a natural bijection between preduals of Y and preduals of L(X,Y) that respect the right L(X)-module structure. If X is reflexive, it follows that there is a unique predual making L(X) into a dual Banach algebra. ... More

The generator problem for Z-stable C*-algebrasJan 18 2012The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebras ... More

Group algebras acting on $L^p$-spacesAug 24 2014Apr 18 2015For $p\in [1,\infty)$ we study representations of a locally compact group $G$ on $L^p$-spaces and $QSL^p$-spaces. The universal completions $F^p(G)$ and $F^p_{\mathrm{QS}}(G)$ of $L^1(G)$ with respect to these classes of representations (which were first ... More

Accurate Non-adiabatic Quantum Dynamics from Pseudospectral Sampling of Time-dependent Gaussian Basis SetsJun 20 2016Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, ... More

Possible Detection of OVI from the LMC Superbubble N70Mar 30 2006We present FUSE observations toward four stars in the LMC superbubble N70 and compare these spectra to those of four comparison targets located in nearby field and diffuse regions. The N70 sight lines show OVI 1032 absorption that is consistently stronger ... More

Variations of Pickup Ion Distributions and their Relation to Interplanetary Conditions and WavesMay 27 2004Nov 29 2004Pickup ion distributions vary substantially on a variety of time scales, although their sources may be relatively steady. This complicates their use as probes of the heliospheric and local interstellar particle populations. Interstellar He+ pickup ion ... More

On Searching for Small Kochen-Specker Vector Systems (extended version)Nov 14 2011Kochen-Specker (KS) vector systems are sets of vectors in R^3 with the property that it is impossible to assign 0s and 1s to the vectors in such a way that no two orthogonal vectors are assigned 0 and no three mutually orthogonal vectors are assigned ... More

The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein MetricsSep 26 2013Jun 17 2014By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from K\"ahler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm for computing ... More

Kinematics of the swimming of SpiroplasmaJun 29 2009\emph{Spiroplasma} swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. ... More

Observing Zitterbewegung in Ultracold AtomsNov 21 2007Dec 21 2007We propose an optical lattice scheme which would permit the experimental observation of Zitterbewegung (ZB) with ultracold, neutral atoms. A four-level "tripod" variant of the usual setup for stimulated Raman adiabatic passage (STIRAP) has been proposed ... More

Hydrodynamic Excitations of Trapped Fermi GasesMay 18 1999Dec 10 1999We discuss collective excitations of a trapped dilute Fermi gas within a hydrodynamic approximation. Analytical results are derived for both high- and low-temperature limits and are applied to $^{40}$K and $^6$Li systems of current experimental interest. ... More

Rethinking generalization requires revisiting old ideas: statistical mechanics approaches and complex learning behaviorOct 26 2017Feb 17 2019We describe an approach to understand the peculiar and counterintuitive generalization properties of deep neural networks. The approach involves going beyond worst-case theoretical capacity control frameworks that have been popular in machine learning ... More

Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for LearningOct 02 2018Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5 and a miniature-AlexNet. ... More

Donovan's conjecture, blocks with abelian defect groups and discrete valuation ringsSep 21 2018Oct 02 2018We give a reduction to quasisimple groups for Donovan's conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring $\mathcal{O}$. Consequences are that Donovan's conjecture holds for $\mathcal{O}$-blocks ... More

The Low-z Intergalactic Medium. III. HI and Metal Absorbers at z<0.4Sep 25 2007Apr 03 2008We conduct an ultraviolet (HST and FUSE) spectroscopic survey of HI (Lyman lines) and seven metal ions (OVI, NV, CIV, CIII, SiIV, SiIII, FeIII) in the low-redshift intergalactic medium (IGM) at z<0.4. We analyzed 650 Lya absorbers over redshift pathlength ... More

The LyB and OVI Forest in the Local UniverseAug 13 2004Intergalactic absorbers along lines of sight to distant quasars are a powerful diagnostic for the evolution and content of the IGM. In this study, we search known low-z Ly-alpha absorption systems for equivalent absorption in higher Lyman lines as well ... More

Multielectron dissociative ionization of molecules by intense laser radiationNov 26 1996We solve the hydrodynamic-ballistic equations of motion for a one-dimensional time-dependent Thomas-Fermi model of Cl_2 exposed to an intense subpicosecond laser field, and observe simultaneous multielectron ionization and molecular dissociation. The ... More

The ISM Interactions of a Runaway LBV Nebula in the LMCMar 27 2001New observations of the Magellanic Cloud Luminous Blue Variable candidate S119 (HD269687) show the relationship of the star to its environs. Echelle spectroscopy and high-resolution HST imagery reveal an expanding bubble centered on the star. This bubble ... More

Extremal Sasakian Geometry on S^3-bundles over Riemann SurfacesFeb 04 2013In this paper we study the Sasakian geometry on S^3-bundles over a Riemann surface of genus g>0 with emphasis on extremal Sasaki metrics. We prove the existence of a countably infinite number of inequivalent contact structures on the total space of such ... More

Sasakian Manifolds with Perfect Fundamental GroupsOct 09 2012Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions greater than 1. These have extremal Sasaki metrics with constant scalar ... More

Algebraic Topology of Calabi-Yau Threefolds in Toric VarietiesMay 02 2006We compute the integral homology (including torsion), the topological K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold hypersurfaces and complete intersections in Gorenstein toric Fano varieties. The methods are purely topological. ... More

Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau ThreefoldsMay 12 2005This proceedings note introduces aspects of the authors' work relating mirror symmetry and integral variations of Hodge structure. The emphasis is on their classification of the integral variations of Hodge structure which can underly families of Calabi-Yau ... More

The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar CurvatureFeb 11 2014Jun 03 2015We describe a general procedure for constructing new Sasaki metrics of constant scalar curvature from old ones. Explicitly, we begin with a regular Sasaki metric of constant scalar curvature on a 2n+1-dimensional compact manifold M and construct a sequence, ... More

An OVI Baryon Census of the Low-z Warm-Hot Intergalactic MediumJan 04 2005Intergalactic absorbers along lines of sight to distant quasars are a powerful diagnostic for the evolution and content of the intergalactic medium (IGM). In this study, we use the FUSE satellite to search 129 known lya absorption systems at z<0.15 toward ... More

Identifying the Baryons in a Multiphase Intergalactic MediumAug 15 2012In this white paper, we summarize current observations of the baryon census at low redshift (Shull, Smith, & Danforth 2012). Measurements of Lya, O-VI, and broad Lya absorbers, together with more careful corrections for metallicity and ionization fraction, ... More

Creating a supersolid in one-dimensional Bose mixturesJun 03 2008Aug 17 2008We identify a one-dimensional supersolid phase in a binary mixture of near-hardcore bosons with weak, local inter-species repulsion. We find realistic conditions under which such a phase, defined here as the coexistence of quasi-superfluidity and quasi-charge ... More

Ideal Gases in Time-Dependent TrapsSep 10 1999We investigate theoretically the properties of an ideal trapped gas in a time-dependent harmonic potential. Using a scaling formalism, we are able to present simple analytical results for two important classes of experiments: free expansion of the gas ... More

Extremal Sasakian Geometry on $T^2\times S^3$ and Related ManifoldsAug 09 2011Dec 13 2012We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on $T^2\times S^3$ and certain related manifolds. These structures occur in bouquets and exhaust the Sasaki cones in all except ... More