Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Critical behavior in a cross-situational lexicon learning scenario

The associationist account for early word learning is based on the co-occurrence between referents and words. Here we introduce a noisy cross-situational learning scenario in which the referent of the uttered word is eliminated from the context with probability gamma, thus modeling the noise produced by out-of-context words. We examine the performance of a simple associative learning algorithm and find a critical value of the noise parameter gamma(c) above which learning is impossible. We use finite-size scaling to show that the sharpness of the transition persists across a region of order tau(-1/2) about gamma(c), where tau is the number of learning trials, as well as to obtain the learning error (scaling function) in the critical region. In addition, we show that the distribution of durations of periods when the learning error is zero is a power law with exponent -3/2 at the critical point. Copyright (C) EPLA, 2012

Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: Partition function zeros approach

We have performed multicanonical simulations to study the critical behavior of the two-dimensional Ising model with dipole interactions. This study concerns the thermodynamic phase transitions in the range of the interaction delta where the phase characterized by striped configurations of width h = 1 is observed. Controversial results obtained from local update algorithms have been reported for this region, including the claimed existence of a second-order phase transition line that becomes first order above a tricritical point located somewhere between delta = 0.85 and 1. Our analysis relies on the complex partition function zeros obtained with high statistics from multicanonical simulations. Finite size scaling relations for the leading partition function zeros yield critical exponents. that are clearly consistent with a single second-order phase transition line, thus excluding such a tricritical point in that region of the phase diagram. This conclusion is further supported by analysis of the specific heat and susceptibility of the orientational order parameter.

Magneto-optical probe of quantum Hall states in a wide parabolic well modulated by random potential

Polarized photoluminescence from weakly coupled random multiple well quasi-three-dimensional electron system is studied in the regime of the integer quantum Hall effect. Two quantum Hall ferromagnetic ground states assigned to the uncorrelated miniband quantum Hall state and to the spontaneous interwell phase coherent dimer quantum Hall state are observed. Photoluminescence associated with these states exhibits features caused by finite-size skyrmions: dramatic reduction of the electron spin polarization when the magnetic field is increased past the filling factor nu = 1. The effective skyrmion size is larger than in two-dimensional electron systems.

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

Heat conduction in a chain of harmonic and anharmonic oscillators under the presence of an energy conserving noise

Reproducing Fourier's law of heat conduction from a microscopic stochastic model is a long standing challenge in statistical physics. As was shown by Rieder, Lebowitz and Lieb many years ago, a chain of harmonically coupled oscillators connected to two heat baths at different temperatures does not reproduce the diffusive behaviour of Fourier's law, but instead a ballistic one with an infinite thermal conductivity. Since then, there has been a substantial effort from the scientific community in identifying the key mechanism necessary to reproduce such diffusivity, which usually revolved around anharmonicity and the effect of impurities. Recently, it was shown by Dhar, Venkateshan and Lebowitz that Fourier's law can be recovered by introducing an energy conserving noise, whose role is to simulate the elastic collisions between the atoms and other microscopic degrees of freedom, which one would expect to be present in a real solid. For a one-dimensional chain this is accomplished numerically by randomly flipping - under the framework of a Poisson process with a variable “rate of collisions" - the sign of the velocity of an oscillator. In this poster we present Langevin simulations of a one-dimensional chain of oscillators coupled to two heat baths at different temperatures. We consider both harmonic and anharmonic (quartic) interactions, which are studied with and without the energy conserving noise. With these results we are able to map in detail how the heat conductivity k is influenced by both anharmonicity and the energy conserving noise. We also present a detailed analysis of the behaviour of k as a function of the size of the system and the rate of collisions, which includes a finite-size scaling method that enables us to extract the relevant critical exponents. Finally, we show that for harmonic chains, k is independent of temperature, both with and without the noise. Conversely, for anharmonic chains we find that k increases roughly linearly with the temperature of a given reservoir, while keeping the temperature difference fixed.

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.

Variance Effective Population Size for Dioecious Species

The concept of effective population size (N(e)) is an important measure of representativeness in many areas. In this research, we consider the statistical properties of the number of contributed gametes under practical situations by adapting Crow and Denninston's (1988) N(e) formulas for dioecious species. Three sampling procedures were considered. In all circumstances, results show that as the offspring sex ratio (r) deviates from 0.5, N(e) values become smaller, and the efficiency of gametic control for increasing N(e) is reduced. For finite populations, where all individuals are potentially functional parents, the reduction in N(e) due to an unequal sex ratio can be compensated for through female gametic control when 0.28 <= r <= 0.72. This outcome is important when r is unknown. When only a fraction of the individuals in a population is taken for reproduction, N(e) is meaningful only if the size of the reference population is clearly defined. Gametic control is a compensating factor in accession regeneration when the viability of the accession is around 70 or 75%. For germ-plasm collection, when parents are a very small fraction of the population, maximum N(e) will be approximately 47 and 57% of the total number of offspring sampled, with female gametic control, r varying between 0.3 and 0.5, and being constant over generations.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.