On the sharpness of the zero-entropy-density conjecture

The zero-entropy-density conjecture states that the entropy density, defined as the limit of S(N)/N at infinity, vanishes for all translation-invariant pure states on the spin chain. Or equivalently, S(N), the von Neumann entropy of such a state restricted to N consecutive spins, is sublinear. In this paper it is proved that this conjecture cannot be sharpened, i.e., translation-invariant states give rise to arbitrary fast sublinear entropy growth. The proof is constructive, and is based on a class of states derived from quasifree states on a CAR algebra. The question whether the entropy growth of pure quasifree states can be arbitrary fast sublinear was first raised by Fannes et al. [J. Math. Phys. 44, 6005 (2003)]. In addition to the main theorem it is also shown that the entropy asymptotics of all pure shift-invariant nontrivial quasifree states is at least logarithmic.Comment: 11 pages, references added, corrected typo

Entanglement entropy and quantum field theory: a non-technical introduction

In these proceedings we give a pedagogical and non-technical introduction to the Quantum Field Theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional Conformal Field Theory.Comment: 10 Pages, 2 figures. Talk given at the conference "Entanglement in Physical and information sciences", Centro Ennio de Giorgi, Pisa, December 200

Distinguishing between Neutrinos and time-varying Dark Energy through Cosmic Time

We study the correlations between parameters characterizing neutrino physics and the evolution of dark energy. Using a fluid approach, we show that time-varying dark energy models exhibit degeneracies with the cosmic neutrino background over extended periods of the cosmic history, leading to a degraded estimation of the total mass and number of species of neutrinos. We investigate how to break degeneracies and combine multiple probes across cosmic time to anchor the behaviour of the two components. We use Planck CMB data and BAO measurements from the BOSS, SDSS and 6dF surveys to present current limits on the model parameters, and then forecast the future reach from the CMB Stage-4 and DESI experiments. We show that a multi-probe analysis of current data provides only marginal improvement on the determination of the individual parameters and no reduction of the correlations. Future observations will better distinguish the neutrino mass and preserve the current sensitivity to the number of species even in case of a time-varying dark energy component.Comment: 10 pages, 7 figures, minor updates to match the version accepted by Phys. Rev.

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

Spinal cord gray matter segmentation using deep dilated convolutions

Gray matter (GM) tissue changes have been associated with a wide range of neurological disorders and was also recently found relevant as a biomarker for disability in amyotrophic lateral sclerosis. The ability to automatically segment the GM is, therefore, an important task for modern studies of the spinal cord. In this work, we devise a modern, simple and end-to-end fully automated human spinal cord gray matter segmentation method using Deep Learning, that works both on in vivo and ex vivo MRI acquisitions. We evaluate our method against six independently developed methods on a GM segmentation challenge and report state-of-the-art results in 8 out of 10 different evaluation metrics as well as major network parameter reduction when compared to the traditional medical imaging architectures such as U-Nets.Comment: 13 pages, 8 figure

Corrections to scaling in entanglement entropy from boundary perturbations

We investigate the corrections to scaling of the Renyi entropies of a region of size l at the end of a semi-infinite one-dimensional system described by a conformal field theory when the corrections come from irrelevant boundary operators. The corrections from irrelevant bulk operators with scaling dimension x have been studied by Cardy and Calabrese (2010), and they found not only the expected corrections of the form l^(4-2x) but also unusual corrections that could not have been anticipated by finite-size scaling arguments alone. However, for the case of perturbations from irrelevant boundary operators we find that the only corrections that can occur to leading order are of the form l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1) when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally irrelevant boundary perturbation will give leading corrections going as log(l)^(-3). No unusual corrections occur when perturbing with a boundary operator.Comment: 8 pages. Minor improvements and updated references. Published versio

Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations

Many alternative formulations of Einstein's evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill-behaved. Specifically, we examine the growth of approximate (geometric-optics) solutions, studied only in the future domain of dependence of the initial data slice (e.g. we study transients). By evaluating the amplification of transients a given formulation will produce, we may therefore eliminate from consideration the most pathological formulations (e.g. those with numerically-unacceptable amplification). This technique has the potential to provide surprisingly tight constraints on the set of formulations one can safely apply. To illustrate the application of these techniques to practical examples, we apply our technique to the 2-parameter family of evolution equations proposed by Kidder, Scheel, and Teukolsky, focusing in particular on flat space (in Rindler coordinates) and Schwarzchild (in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.

Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any integer n is calculated as the four-point function of a particular type of twist fields and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos corrected and refs adde

Quantum Quench from a Thermal Initial State

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor change

The role of initial conditions in the ageing of the long-range spherical model

The kinetics of the long-range spherical model evolving from various initial states is studied. In particular, the large-time auto-correlation and -response functions are obtained, for classes of long-range correlated initial states, and for magnetized initial states. The ageing exponents can depend on certain qualitative features of initial states. We explicitly find the conditions for the system to cross over from ageing classes that depend on initial conditions to those that do not.Comment: 15 pages; corrected some typo