Two-Scale Annihilation

The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between convection and diffusion leads to a decay of the density which is proportional to $t^{-3/4}$. At long times, the reactants organize into domains of right- and left-moving particles, with the typical distance between particles in a single domain growing as $t^{3/4}$, and the distance between domains growing as $t$. The probability that an arbitrary particle reacts with its $n^{\rm th}$ neighbor is found to decay as $n^{-5/2}$ for same-velocity pairs and as $n^{-7/4}$ for $+-$ pairs. These kinetic and spatial exponents and their interrelations are obtained by scaling arguments. Our predictions are in excellent agreement with numerical simulations.Comment: revtex, 5 pages, 5 figures, also available from http://arnold.uchicago.edu/~eb

Open String Wavefunctions in Warped Compactifications

We analyze the wavefunctions for open strings in warped compactifications, and compute the warped Kahler potential for the light modes of a probe D-brane. This analysis not only applies to the dynamics of D-branes in warped backgrounds, but also allows to deduce warping corrections to the closed string Kahler metrics via their couplings to open strings. We consider in particular the spectrum of D7-branes in warped Calabi-Yau orientifolds, which provide a string theory realizations of the Randall-Sundrum scenario. We find that certain background fluxes, necessary in the presence of warping, couple to the fermionic wavefunctions and qualitatively change their behavior. This modified dependence of the wavefunctions are needed for consistency with supersymmetry, though it is present in non-supersymmetric vacua as well. We discuss the deviations of our setup from the RS scenario and, as an application of our results, compute the warping corrections to Yukawa couplings in a simple model. Our analysis is performed both with and without the presence of D-brane world-volume flux, as well as for the case of backgrounds with varying dilaton.Comment: 52 pages, refs. added, minor correction

A Field Range Bound for General Single-Field Inflation

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models. This shows that non-trivial dynamics can't evade the Lyth bound. We also present a weaker, but completely universal bound that holds whenever the Null Energy Condition (NEC) is satisfied at horizon crossing.Comment: 16 page

Generating Function for Particle-Number Probability Distribution in Directed Percolation

We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single particle on a lattice, we show that the GF of the PNPD can be written as an infinite series of cumulants taken at zero momentum. This series can be summed up into a complete form at the level of a mean-field approximation. Using the renormalization group techniques, we determine logarithmic corrections for the GF at the upper critical dimension. We also find the critical scaling form for the PNPD and check its universality numerically in one dimension. The critical scaling function is found to be universal up to two non-universal metric factors.Comment: (v1,2) 8 pages, 5 figures; one-loop calculation corrected in response to criticism received from Hans-Karl Janssen, (v3) content as publishe

Scale-Invariance and the Strong Coupling Problem

The effective theory of adiabatic fluctuations around arbitrary Friedmann-Robertson-Walker backgrounds - both expanding and contracting - allows for more than one way to obtain scale-invariant two-point correlations. However, as we show in this paper, it is challenging to produce scale-invariant fluctuations that are weakly coupled over the range of wavelengths accessible to cosmological observations. In particular, requiring the background to be a dynamical attractor, the curvature fluctuations are scale-invariant and weakly coupled for at least 10 e-folds only if the background is close to de Sitter space. In this case, the time-translation invariance of the background guarantees time-independent n-point functions. For non-attractor solutions, any predictions depend on assumptions about the evolution of the background even when the perturbations are outside of the horizon. For the simplest such scenario we identify the regions of the parameter space that avoid both classical and quantum mechanical strong coupling problems. Finally, we present extensions of our results to backgrounds in which higher-derivative terms play a significant role.Comment: 17 pages + appendices, 3 figures; v2: typos fixe

Method for Generating Additive Shape Invariant Potentials from an Euler Equation

In the supersymmetric quantum mechanics formalism, the shape invariance condition provides a sufficient constraint to make a quantum mechanical problem solvable; i.e., we can determine its eigenvalues and eigenfunctions algebraically. Since shape invariance relates superpotentials and their derivatives at two different values of the parameter $a$, it is a non-local condition in the coordinate-parameter $(x, a)$ space. We transform the shape invariance condition for additive shape invariant superpotentials into two local partial differential equations. One of these equations is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow. The second equation provides the constraint that helps us determine unique solutions. We solve these equations to generate the set of all known $\hbar$-independent shape invariant superpotentials and show that there are no others. We then develop an algorithm for generating additive shape invariant superpotentials including those that depend on $\hbar$ explicitly, and derive a new $\hbar$-dependent superpotential by expanding a Scarf superpotential.Comment: 1 figure, 4 tables, 18 page

Next-to-leading order QCD corrections to W+W- production via vector-boson fusion

Vector-boson fusion processes constitute an important class of reactions at hadron colliders, both for signals and backgrounds of new physics in the electroweak interactions. We consider what is commonly referred to as W+W- production via vector-boson fusion (with subsequent leptonic decay of the Ws), or, more precisely, e+ nu_e mu- nubar_mu + 2 jets production in proton-proton scattering, with all resonant and non-resonant Feynman diagrams and spin correlations of the final-state leptons included, in the phase-space regions which are dominated by t-channel electroweak-boson exchange. We compute the next-to-leading order QCD corrections to this process, at order alpha^6 alpha_s. The QCD corrections are modest, changing total cross sections by less than 10%. Remaining scale uncertainties are below 2%. A fully-flexible next-to-leading order partonic Monte Carlo program allows to demonstrate these features for cross sections within typical vector-boson-fusion acceptance cuts. Modest corrections are also found for distributions.Comment: 29 pages, 14 figure

VerdictDB: Universalizing Approximate Query Processing

Despite 25 years of research in academia, approximate query processing (AQP) has had little industrial adoption. One of the major causes of this slow adoption is the reluctance of traditional vendors to make radical changes to their legacy codebases, and the preoccupation of newer vendors (e.g., SQL-on-Hadoop products) with implementing standard features. Additionally, the few AQP engines that are available are each tied to a specific platform and require users to completely abandon their existing databases---an unrealistic expectation given the infancy of the AQP technology. Therefore, we argue that a universal solution is needed: a database-agnostic approximation engine that will widen the reach of this emerging technology across various platforms. Our proposal, called VerdictDB, uses a middleware architecture that requires no changes to the backend database, and thus, can work with all off-the-shelf engines. Operating at the driver-level, VerdictDB intercepts analytical queries issued to the database and rewrites them into another query that, if executed by any standard relational engine, will yield sufficient information for computing an approximate answer. VerdictDB uses the returned result set to compute an approximate answer and error estimates, which are then passed on to the user or application. However, lack of access to the query execution layer introduces significant challenges in terms of generality, correctness, and efficiency. This paper shows how VerdictDB overcomes these challenges and delivers up to 171$\times$ speedup (18.45$\times$ on average) for a variety of existing engines, such as Impala, Spark SQL, and Amazon Redshift, while incurring less than 2.6% relative error. VerdictDB is open-sourced under Apache License.Comment: Extended technical report of the paper that appeared in Proceedings of the 2018 International Conference on Management of Data, pp. 1461-1476. ACM, 201

Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit

We estimate analytically the second-order cosmic microwave background temperature anisotropies at the recombination epoch in the squeezed limit and we deduce the contamination to the primordial local non-Gaussianity. We find that the level of contamination corresponds to f_NL^{con}=O(1) which is below the sensitivity of present experiments and smaller than the value O(5) recently claimed in the literature.Comment: LaTeX file; 15 pages. Slightly revised version. Main result unchange

Ghost Condensation and a Consistent Infrared Modification of Gravity

We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from ghost condensation--a background where a scalar field \phi has a constant velocity, = M^2. The ghost condensate is a new kind of fluid that can fill the universe, which has the same equation of state, \rho = -p, as a cosmological constant, and can hence drive de Sitter expansion of the universe. However, unlike a cosmological constant, it is a physical fluid with a physical scalar excitation, which can be described by a systematic effective field theory at low energies. The excitation has an unusual low-energy dispersion relation \omega^2 \sim k^4 / M^2. If coupled to matter directly, it gives rise to small Lorentz-violating effects and a new long-range 1/r^2 spin dependent force. In the ghost condensate, the energy that gravitates is not the same as the particle physics energy, leading to the possibility of both sources that can gravitate and antigravitate. The Newtonian potential is modified with an oscillatory behavior starting at the distance scale M_{Pl}/M^2 and the time scale M_{Pl}^2/M^3. This theory opens up a number of new avenues for attacking cosmological problems, including inflation, dark matter and dark energy.Comment: 42 pages, LaTeX 2