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Primordial black holes as dark matter and generators of cosmic structureJan 23 2019Primordial black holes (PBHs) could provide the dark matter but a variety of constraints restrict the possible mass windows to $10^{16} - 10^{17}$g, $10^{20} - 10^{24}$g and $10 - 10^3M_{\odot}$. The last possibility is of special interest in view of ... More

Dynamical trapping of light in harmonically breathing waveguide latticesFeb 13 2019A new strategy for trapping quantum particles is presented, which allow us to simulate an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed point ... More

Two-generator subgroups of right-angled Artin groups are quasi-isometrically embeddedDec 01 2014Oct 13 2015We show that non-abelian two-generator subgroups of right-angled Artin groups are quasi-isometrically embedded free groups. This provides an alternate proof of a theorem of A. Baudisch: that all two-generator subgroups are free or free abelian. Additionally, ... More

Baryonic and Non-Baryonic Dark MatterAug 01 2000Cosmological nucleosynthesis calculations imply that there should be both non-baryonic and baryonic dark matter. Recent data suggest that some of the non-baryonic dark matter must be "hot" (i.e. massive neutrinos) and there may also be evidence for "cold" ... More

A polygonal presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$Nov 13 2009In the first section of this article, we recall Keel's well-known presentation of $Pic(\overline{\mathfrak{M}}_{0,n})$ using irreducible boundary divisors of $\overline{\mathfrak{M}}_{0,n}$ as generators, and describe a basis for $Pic(\overline{\mathfrak{M}}_{0,n})$ ... More

Multizeta values: Lie algebras and periods on $\mathfrak{M}_{0,n}$Nov 13 2009This thesis is a study of algebraic and geometric relations between multizeta values. In chapter 2, we prove a result which gives the dimension of the associated depth-graded pieces of the double shuffle Lie algebra in depths 1 and 2. In chapters 3 and ... More

Periods on the moduli space of genus 0 curvesNov 13 2009This report outlines a combinatorial recipe for computing the bases, whose elements are oriented polygons, of two cohomology spaces associated to multizeta values: the top dimensional de Rham cohomology of moduli spaces of genus 0 complex pointed curves ... More

Non Trivial Effects in Heavy Nuclear Systems due to Charge RearrangementSep 27 2003Dec 04 2003In this report we propose that a charge rearrangement within heavy ions may occur during fusion reactions, lowering the Coulomb barrier as the nuclear systems approach each other. In this situation a modified Gamow factor has been calculated, which emphasizes ... More

Super-Razor and Searches for Sleptons and Charginos at the LHCOct 17 2013Direct searches for electroweak pair production of new particles at the LHC are a difficult proposition, due to the large background and low signal cross sections. We demonstrate how these searches can be improved by a combination of new razor variables ... More

Robust replication of barrier-style claims on price and volatilityAug 04 2015We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\<X\>$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky ... More

Primordial Black Holes With Multi-Modal Mass SpectraNov 15 2018A mechanism for generating primordial black hole mass spectra with many spikes is proposed and investigated. This mechanism relies on the choice of non-Bunch-Davies vacua, these leading to oscillatory features in the inflationary power spectrum. This ... More

Primordial Black Holes - Recent DevelopmentsApr 01 2005Recent developments in the study of primordial black holes (PBHs) will be reviewed, with particular emphasis on their formation and evaporation. PBHs could provide a unique probe of the early Universe, gravitational collapse, high energy physics and quantum ... More

A classification of spherically symmetric self-similar dust modelsMar 02 2000We classify all spherically symmetric dust solutions of Einstein's equations which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. We show that the equations can be reduced to a special case of the general ... More

Recent developments in the search for baryonic dark matterFeb 22 2001Mar 20 2001Cosmological nucleosynthesis calculations imply that many of the baryons in the Universe must be dark. We discuss the likelihood that some of these dark baryons may reside in galaxies as Massive Compact Halo Objects (MACHOs), the remnants of a first generation ... More

Characteristic time scales for diffusion processes through layers and across interfacesJan 16 2018Apr 12 2018This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, ... More

Calculating how long it takes for a diffusion process to effectively reach steady state without computing the transient solutionApr 21 2017Jul 11 2017Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} transition time, defined as the time required for the transient solution to ... More

On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisitedFeb 09 2001The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial ... More

The Black Hole Uncertainty Principle CorrespondenceFeb 06 2014The Black Hole Uncertainty Principle correspondence proposes a connection between the Uncertainty Principle on microscopic scales and black holes on macroscopic scales. This is manifested in a unified expression for the Compton wavelength and Schwarzschild ... More

Baryonic Dark Matter in GalaxiesAug 01 2000Cosmological nucleosynthesis calculations imply that many of the baryons in the Universe must be dark. We discuss the likelihood that some of these dark baryons may reside in the discs or halos of galaxies. If they were in the form of compact objects, ... More

Spherically symmetric self-similar solutions and their astrophysical and cosmological applicationsMar 02 2000We discuss spherically symmetric perfect fluid solutions of Einstein's equations which have equation of state ($p=\alpha \mu$) and which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. For each value of $\alpha$, ... More

Advection improves homogenized models of continuum diffusion in one-dimensional heterogeneous mediaAug 07 2019We propose a novel homogenization method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized equation ... More

ADOL - Markovian approximation of rough lognormal modelApr 19 2019In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift ... More

Local Variance Gamma and Explicit Calibration to Option PricesAug 10 2013Jan 31 2014In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for calibrating ... More

Using pseudo-parabolic and fractional equations for option pricing in jump diffusion modelsFeb 09 2010In mathematical finance a popular approach for pricing options under some Levy model is to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually ... More

Concerning the Representability of Self-Reference in ArithmeticSep 05 2011Jan 27 2012Terms in arithmetic of the form s in the formula s=t(< s >), with t a term with one free variable and < s > a numeral denoting the G\"odel number of s, are examined by writing the explicit definition of the encoding functions whose representation they ... More

FX Options in Target ZoneDec 04 2015Jul 28 2016In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) ... More

A classical picture of lepton neutral current forcesMar 11 1999When charged current weak interations are excluded, the neutral current weak interaction is formally similar to ordinary electromagnetism with a massive photon. In this spirit, the Maxwell equations for the fields of the Z-boson are derived from the standard ... More

Primordial Black Holes and Quantum EffectsFeb 06 2014Primordial black holes (PBHs) are of special interest because of the crucial role of quantum effects in their formation and evaporation. This means that they provide a unique probe of the early universe, high-energy physics and quantum gravity. We highlight ... More

On the initial-value problem of the Maxwell-Lorentz equationsJul 06 2010Oct 03 2010We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and ... More

Geometric Local Variance Gamma modelSep 19 2018Dec 25 2018This paper describes another extension of the Local Variance Gamma model originally proposed by P. Carr in 2008, and then further elaborated on by Carr and Nadtochiy, 2017 (CN2017), and Carr and Itkin, 2018 (CI2018). As compared with the latest version ... More

Complete graph decompositions and p-groupoidsApr 09 2019We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize P-groupoids when the corresponding decomposition is a Hamiltonian decomposition for ... More

Bessel processes, the integral of geometric Brownian motion, and Asian optionsNov 17 2003This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions about exponential ... More

Primordial black holes as a probe of the early universe and a varying gravitational constantFeb 22 2001Mar 20 2001We discuss recent developments in the study of primordial black holes, focussing particularly on their formation and quantum evaporation. Such studies can place important constraints on models of the early Universe. An especially interesting development ... More

Quantum Black Holes as the Link Between Microphysics and MacrophysicsMar 25 2017There appears to be a duality between elementary particles, which span the mass range below the Planck scale, and black holes, which span the mass range range above it. In particular, the Black Hole Uncertainty Principle Correspondence posits a smooth ... More

Primordial Black Holes With Multi-Modal Mass SpectraNov 15 2018May 29 2019A mechanism for generating primordial black-hole mass spectra with many spikes is proposed and investigated. This mechanism relies on the choice of non-Bunch-Davies vacua, these leading to oscillatory features in the inflationary power spectrum. This ... More

Strong correlation effects in single-wall carbon nanotubesNov 07 2008We present an overview of strong correlations in single-wall carbon nanotubes, and an introduction to the techniques used to study them theoretically. We concentrate on zigzag nanotubes, although universality dictates that much ofthe theory can also be ... More

Primordial Black Holes as a Probe of Cosmology and High Energy PhysicsOct 29 2003Recent developments in the study of primordial black holes (PBHs) will be reviewed, with particular emphasis on their formation and evaporation. PBHs could provide a unique probe of the early Universe, gravitational collapse, high energy physics and quantum ... More

Primordial Black Holes: Do They Exist and Are They Useful?Nov 26 2005Recent developments in the study of primordial black holes (PBHs) are reviewed, with particular emphasis on their formation and evaporation. It is still not clear whether PBHs formed but, if they did, they could provide a unique probe of the early Universe, ... More

Primordial Black Holes as Generators of Cosmic StructuresJan 02 2018Jun 23 2018Primordial black holes (PBHs) could provide the dark matter in various mass windows below $10^2 M_{\odot}$ and those of $30 M_{\odot}$ might explain the LIGO events. PBHs much larger than this might have important consequences even if they provide only ... More

Geometries, the principle of duality, and algebraic groupsMar 10 2005Sep 09 2005Jacques Tits gave a general recipe for producing an abstract geometry from a semisimple algebraic group. This expository paper describes a uniform method for giving a concrete realization of Tits's geometry and works through several examples. We also ... More

A lognormal type stochastic volatility model with quadratic driftAug 20 2019This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant ... More

Upper limits on the size of a primordial black holeDec 06 2004May 11 2005We provide precise constraints on the size of any black holes forming in the early Universe for a variety of formation scenarios. In particular, we prove that the size of the apparent horizon of a primordial black hole formed by causal processes in a ... More

On the Linear Independence of RootsMar 19 2007Sep 14 2007A set of real $n$th roots that is pairwise linearly independent over the rationals must also be linearly independent. We show how this result may be extended to more general fields.

Higher-order quantum bright solitons in Bose-Einstein condensates show truly quantum emergent behaviorDec 16 2016When an interaction quench by a factor of four is applied to an attractive Bose-Einstein condensate, a higher-order quantum bright soliton exhibiting robust oscillations is predicted in the semiclassical limit by the Gross-Pitaevskii equation. Combining ... More

Super-horizon primordial black holesAug 04 2005Aug 24 2005We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. ... More

On flips of unitary buildings I: Classification of flipsDec 10 2010We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related to flips and ... More

The Compton-Schwarzschild relations in higher dimensionsNov 07 2016Dec 31 2018In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$) and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there is a fundamental ... More

Limits of sympathetic cooling of fermions: The role of the heat capacity of the coolantOct 28 2003Jun 16 2004The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below $T_c$ is by no means reduced when its heat capacity ... More

Dynamics of a matter-wave bright soliton in an expulsive potentialMay 29 2002May 31 2002The stability regimes and nonlinear dynamics of bright solitons created in a harmonic potential which is transversely attractive and longitudinally expulsive are presented. This choice of potential is motivated by the recent creation of a matter-wave ... More

The Compton-Schwarzschild relations in higher dimensionsNov 07 2016In three spatial dimensions, the Compton wavelength $(R_C \propto M$) and Schwarzschild radius $(R_S \propto M^{-1}$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there is a fundamental ... More

Emergent topological properties in interacting one-dimensional systems with spin-orbit couplingApr 20 2015Jul 27 2015We present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy theory is ... More

A THz time-domain susceptibility for superconductors including strong-current effectsJul 19 2013Oct 08 2013Finite-difference time-domain methods are increasingly being used to develop, model and analyze the response of materials, including engineered metamaterials that may contain superconductors. Though simple and useful expressions for the time-domain susceptibility ... More

Spacetime structure of self-similar spherically symmetric perfect fluid solutionsSep 24 2002Dec 09 2002We classify all spherically symmetric and homothetic spacetimes that are allowed kinematically by constructing them from a small number of building blocks. We then restrict attention to a particular dynamics, namely perfect fluid matter with the scale-free ... More

Graph Neural Processes: Towards Bayesian Graph Neural NetworksFeb 26 2019We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of sparsely observed ... More

Coxeter Complexes and Graph-AssociahedraJul 13 2004Dec 09 2005Given a graph G, we construct a simple, convex polytope whose face poset is based on the connected subgraphs of G. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial ... More

Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug deliveryJan 16 2018We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing ... More

The separate universe problem: 40 years onMay 14 2014The claim that an overdense (positive curvature) region in the early universe cannot extend beyond some maximum scale and remain part of our universe, first made 40 years ago, has recently been questioned by Kopp et al. Their analysis is elucidating and ... More

Preparation of entangled and antiferromagnetic states by dissipative Rydberg pumpingApr 23 2013Jun 06 2013We propose and analyze an approach for preparation of high fidelity entanglement and antiferromagnetic states using Rydberg mediated interactions with dissipation. Using asymmetric Rydberg interactions the two-atom Bell singlet is a dark state of the ... More

The Compton-Schwarzschild correspondence from extended de Broglie relationsMay 26 2015Apr 05 2016The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial ... More

Quantum teleportation between nanomechanical modesDec 19 2005We study a quantum teleportation scheme between two nanomechanical modes without local interaction. The nanomechanical modes are linearly coupled to and connected by the continuous variable modes of a superconducting circuit consisting of a transmission ... More

Nucleation of superfluid-light domains in a quenched dynamicsFeb 03 2018Aug 15 2018Strong correlation effects emerge from light-matter interactions in coupled resonator arrays, such as the Mott-insulator to superfluid phase transition of atom-photon excitations. We demonstrate that the quenched dynamics of a finite-sized complex array ... More

Growth of primordial black holes in a universe containing a massless scalar fieldDec 06 2004May 11 2005The evolution of primordial black holes in a flat Friedmann universe with a massless scalar field is investigated in fully general relativistic numerical relativity. A primordial black hole is expected to form with a scale comparable to the cosmological ... More

Doubly magic optical trapping for Cs atom hyperfine clock transitionsJun 13 2014Sep 19 2016We analyze doubly magic trapping of Cs hyperfine transitions including previously neglected contributions from the ground state hyperpolarizability and the interaction of the laser light and a static magnetic field. Extensive numerical searches do not ... More

Does Compton/Schwarzschild duality in higher dimensions exclude TeV quantum gravity?Aug 25 2018Dec 31 2018In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$) and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there could be a fundamental ... More

Drug delivery from microcapsules: how can we estimate the release time?Jan 24 2019Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external ... More

Driven two-component Bose-Einstein condensate in optical latticesOct 28 2016Oct 31 2016We explore quantum many-body physics of a driven Bose-Einstein condensate and present exact results for the Rabi-Bogoliubov spectrum and amplitudes of the condensate. We find a gap in the spectrum of elementary excitations that amounts to the effective ... More

Description of Induced Nuclear Fission with Skyrme Energy Functionals: II. Finite Temperature EffectsNov 11 2013Jan 23 2015Understanding the mechanisms of induced nuclear fission for a broad range of neutron energies could help resolve fundamental science issues, such as the formation of elements in the universe, but could have also a large impact on societal applications ... More

The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysisFeb 13 2014Feb 15 2015The nonlinear Dirac equation for Bose-Einstein condensates in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of ... More

Exact equilibrium results in the Interacting Resonant Level ModelOct 18 2018Jan 08 2019We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the Numerical Renormalization Group and Density Matrix Renormalization Group were performed in order to compare with ... More

Spectrum and correlation functions of a quasi-one-dimensional quantum Ising modelDec 11 2002Mar 25 2003We consider a model of weakly coupled quantum Ising chains. We describe the phase diagram of such a model and study the dynamical magnetic susceptibility by means of Bethe ansatz and the Random Phase Approximation applied to the inter-chain exchange. ... More

Generalized Uncertainty Principle and Self-dual Black HolesJul 04 2011The Generalized Uncertainty Principle suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It provides a natural transition between the expressions for the Compton wavelength below the Planck mass and the ... More

Self-similar cosmological solutions with dark energy. I: formulation and asymptotic analysisJul 04 2007Jan 02 2008Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation ... More

Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditionsMay 28 2017Apr 25 2018We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical ... More

Accurate and efficient calculation of response times for groundwater flowJul 20 2017Feb 09 2018We study measures of the amount of time required for transient flow in heterogeneous porous media to effectively reach steady state, also known as the response time. Here, we develop a new approach that extends the concept of mean action time. Previous ... More

Rapid calculation of maximum particle lifetime for diffusion in complex geometriesJan 09 2018Feb 21 2018Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an absorbing boundary. ... More

Persistent Black Holes in Bouncing CosmologiesJan 20 2017Jun 07 2017In this paper we explore the idea that black holes can persist in a universe that collapses to a big crunch and then bounces into a new phase of expansion. We use a scalar field to model the matter content of such a universe {near the time} of the bounce, ... More

Microscopic model for Feshbach interacting fermions in an optical lattice with arbitrary scattering length and resonance widthSep 07 2011Dec 12 2012We numerically study the problem of two fermions in a three dimensional optical lattice interacting via a zero-range Feshbach resonance, and display the dispersions of the bound states as a two-particle band structure with unique features compared to ... More

Sub-Planckian black holes and the Generalized Uncertainty PrincipleApr 28 2015Jul 17 2015The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like ... More

Primordial black holes from inflaton and spectator field perturbations in a matter-dominated eraJun 12 2017Sep 04 2017We study production of primordial black holes (PBHs) during an early matter-dominated phase. As a source of perturbations, we consider either the inflaton field with a running spectral index or a spectator field that has a blue spectrum and thus provides ... More

On the Hedging of Options On Exploding Exchange RatesFeb 28 2012Nov 24 2013We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows ... More

Primordial black holes, dark matter and hot-spot electroweak baryogenesis at the quark-hadron epochApr 03 2019We propose a scenario in which the quantum fluctuations of a light stochastic spectator field during inflation, for instance the QCD axion, generate large curvature fluctuations in the radiation era. This inevitably leads to the existence of Hubble patches ... More

Rear-surface integral method for calculating thermal diffusivity: finite pulse time correction and two-layer samplesApr 05 2019We study methods for calculating the thermal diffusivity of solids from laser flash experiments. This experiment involves subjecting the front surface of a small sample of the material to a heat pulse and recording the resulting temperature rise on the ... More

From Stars to Super-planets: the Low-Mass IMF in the Young Cluster IC348May 12 2000We investigate the low-mass population of the young cluster IC348 down to the deuterium-burning limit, a fiducial boundary between brown dwarf and planetary mass objects, using a new and innovative method for the spectral classification of late-type objects. ... More

Limits of sympathetic cooling of fermions by zero temperature bosons due to particle lossesMay 19 2003Feb 23 2004It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403 (2001)] that loss of fermions in a degenerate system causes strong heating. We address the fundamental limit imposed by this loss on the temperature that may be obtained by sympathetic ... More

Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensatesJun 19 2010Jan 05 2011We present relativistic linear stability equations (RLSE) for quasi-relativistic cold atoms in a honeycomb optical lattice. These equations are derived from first principles and provide a method for computing stabilities of arbitrary localized solutions ... More

The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and SymmetriesMar 20 2008We show that Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve ... More

Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov AnalysesJan 28 2009May 10 2010We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we treat the one-dimensional ... More

Primordial Black Holes as Dark MatterJul 20 2016Oct 07 2016The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at $10^{16}$ - $10^{17}\,$g, $10^{20}$ - $10^{24}\,$g and $1$ - $10^{3}\,M_{\odot}$. The Planck ... More

Domain Adaptation through Synthesis for Unsupervised Person Re-identificationApr 26 2018Drastic variations in illumination across surveillance cameras make the person re-identification problem extremely challenging. Current large scale re-identification datasets have a significant number of training subjects, but lack diversity in lighting ... More

Topological Winding and Unwinding in Metastable Bose-Einstein CondensatesApr 24 2007Feb 12 2008Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate ... More

Metastable Quantum Phase Transitions in a One-Dimensional Bose GasMay 05 2010Jul 28 2010This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One ... More

Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholesJul 04 2007Jan 02 2008We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid ... More

Tolman-Bondi collapse in scalar-tensor theories as a probe of gravitational memoryDec 31 2001Oct 08 2002In cosmological models with a varying gravitational constant, it is not clear whether primordial black holes preserve the value of $G$ at their formation epoch. We investigate this question by using the Tolman-Bondi model to study the evolution of a background ... More

An asymptotic analysis of spherically symmetric perfect fluid self-similar solutionsAug 01 2000The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1<alpha<1) are described. We prove that for large and small values of the similarity variable, z=r/t, all such solutions must have ... More

Probing the Galactic Dark Matter Mass Funtion Using Microlensing and Direct SearchesDec 02 1994If compact baryonic objects contribute significantly to the dark matter in our Galaxy, their mass function will present vital clues for galaxy formation theories and star formation processes in the early Universe. Here we discuss what one might expect ... More

Out of equilibrium dynamics with Matrix Product StatesMay 04 2012Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of entanglement-restricted states ... More

Primordial Black Holes as Dark MatterJul 20 2016Mar 22 2017The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at $10^{16}$ - $10^{17}\,$g, $10^{20}$ - $10^{24}\,$g and $1$ - $10^{3}\,M_{\odot}$. The Planck ... More

A data driven network approach to rank countries production diversity and food specializationJun 03 2016The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science to disentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use to country ... More

Black holes as echoes of previous cosmic cyclesApr 10 2017The existence of exact solutions which represent a lattice of black holes at a scalar-field-dominated cosmological bounce suggests that black holes could persist through successive eras of a cyclic cosmology. Here we explore some remarkable cosmological ... More

Evolutionary genomics of transposable elements in Saccharomyces cerevisiaeSep 01 2012Saccharomyces cerevisiae is one of the premier model systems for studying the genomics and evolution of transposable elements. The availability of the S. cerevisiae genome led to many insights into its five known transposable element families (Ty1-Ty5) ... More