Renyi entropy, stationarity, and entanglement of the conformal scalar

We extend previous work on the perturbative expansion of the Renyi entropy, $S_q$, around $q=1$ for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Renyi entropies. On the other hand, the perturbative results agree with known Renyi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Renyi entropy of ${\cal N}=4$ super-Yang-Mills near $q=1$. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.Comment: 37 page

Seasonal Time Series and Autocorrelation Function Estimation

Time series are demeaned when sample autocorrelation functions are computed. By the same logic it would seem appealing to remove seasonal means from seasonal time series before computing sample autocorrelation functions. Yet, standard practice is only to remove the overall mean and ignore the possibility of seasonal mean shifts in the data. Whether or not time series are seasonally demeaned has very important consequences on the asymptotic behavior of autocorrelation functions (henceforth ACF). Hasza (1980) and Bierens (1993) studied the asymptotic properties of the sample ACF of non-seasonal integrated processes and showed how they depend on the demeaning of the data. In this paper we study the large sample behavior of the ACF when the data generating processes are seasonal with or without seasonal unit roots. The effect on the asymptotic distribution of seasonal mean shifts and their removal is investigated and the practical consequences of these theoretical developments are also discussed. We also examine the small sample behavior of ACF estimates through Monte Carlo simulations. Lorsqu'on calcule une fonction d'autocorrélation, il est normal d'enlever d'une série la moyenne non conditionnelle. Cette pratique s'applique également dans le cas des séries saisonnières. Pourtant, il serait plus logique d'utiliser des moyennes saisonnières. Hasza (1980) et Bierens (1993) ont étudié l'effet de la moyenne sur l'estimation d'une fonction d'autocorrélation pour un processus avec racine unitaire. Nous examinons le cas de processus avec racines unitaires saisonnières. Nos résultats théoriques de distribution asymptotique, de même que nos simulations de petits échantillons, démontrent l'importance d'enlever les moyennes saisonnières quand on veut identifier proprement les processus saisonniers.Deterministic/stochastic seasonality, model identification, seasonal unit roots, autocorrelation, Saisonalité stochastique et déterministe, identification de modèles, racines unitaires saisonnières,

The Positive Case for Centralization in Health Care Regulation: The Federalism Failures of the ACA

Although the ACA accomplishes significantly greater centralization of authority for healthcare regulation, it falls far short of the full centralization that seems functionally justified. There is no doubt that the states have played an important role in healthcare regulation throughout the nation\u27s history, but that role is becoming increasingly irrelevant as healthcare regulation becomes increasingly technocratic—i.e., increasingly objectivist and data-driven. The ACA is a step in the right direction, but the U.S. should further centralize authority over healthcare

X-ray edge problem of graphene

The X-ray edge problem of graphene with the Dirac fermion spectrum is studied. At half-filling the linear density of states suppresses the singular response of the Fermi liquid, while away from half-filling the singular features of the Fermi liquid reappear. The crossover behavior as a function of the Fermi energy is examined in detail. The exponent of the power-law absorption rate depends both on the intra- and inter-valley scattering, and it changes as a function of the Fermi energy, which may be tested experimentally.Comment: 7 pages, 1 figur

Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State

We examine the long wave length limit of the self-consistent Hartree-Fock approximation irreducible static density-density response function by evaluating the charge induced by an external charge. Our results are consistent with the compressibility sum rule and inconsistent with earlier work that did not account for consistency between the exchange-local-field and the disorder potential. We conclude that the thermodynamic density of states is finite, in spite of the vanishing tunneling density of states at the critical energy of the integer quantum Hall transition.Comment: 5 pages, 4 figures, minor revisions, published versio

Non-meanfield deterministic limits in chemical reaction kinetics far from equilibrium

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte-Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.Comment: 4 pages, 4 figures (submitted to Phys. Rev. Lett.

Anomalous Exponent of the Spin Correlation Function of a Quantum Hall Edge

The charge and spin correlation functions of partially spin-polarized edge electrons of a quantum Hall bar are studied using effective Hamiltonian and bosonization techniques. In the presence of the Coulomb interaction between the edges with opposite chirality we find a different crossover behavior in spin and charge correlation functions. The crossover of the spin correlation function in the Coulomb dominated regime is characterized by an anomalous exponent, which originates from the finite value of the effective interaction for the spin degree of freedom in the long wavelength limit. The anomalous exponent may be determined by measuring nuclear spin relaxation rates in a narrow quantum Hall bar or in a quantum wire in strong magnetic fields.Comment: 4 pages, Revtex file, no figures. To appear in Physical Revews B, Rapid communication