Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate

We derive a set of equations that describe the shape and behaviour of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform a relation for a vortex's velocity, anywhere along the line, is found in terms of the trapping, rotation, and distortion of the line at that location. This relation is then used to find a set of differential equations that give the line's specific shape and motion. This work corrects a previous similar derivation by Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617 (2000)], and enables a comparison with recent numerical results.Comment: 12 pages with 3 figure

High order analysis of the limit cycle of the van der Pol oscillator

We have applied the Lindstedt-Poincaré method to study the limit cycle of the van der Pol oscillator, obtaining the numerical coefficients of the series for the period and for the amplitude to order 859. Hermite-Padé approximants have been used to extract the location of the branch cut of the series with unprecedented accuracy (100 digits). Both series have then been resummed using an approach based on Padé approximants, where the exact asymptotic behaviors of the period and the amplitude are taken into account. Our results improve drastically all previous results obtained on this subject.Fil: Amore, Paolo. Universidad de Colima; MéxicoFil: Boyd, John P.. University of Michigan; Estados UnidosFil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin

Predicting young adult social functioning from developmental trajectories of externalizing behavior

Background. The long-term consequences of child and adolescent externalizing problems often involve a wide spectrum of social maladaptation in adult life. The purpose of this study was to describe the predictive link of child and adolescent externalizing developmental trajectories to social functioning in adulthood. Method. Social functioning was predicted from developmental trajectories of parent-reported aggression, opposition, property violations and status violations that were defined in a longitudinal multiple birth cohort study of 2076 males and females aged 4-18 years. Social functioning was assessed using self-reports by young adults aged 18-30 years. Linear and logistic regression analyses were used to describe the extent to which developmental trajectories are prospectively related to social functioning. Results. Children with high-level trajectories of opposition and status violations reported more impaired social functioning as young adults than children with high-level trajectories of aggression and property violations. Young adults who showed onset of problems in adolescence reported overall less impaired social functioning than individuals with high-level externalizing problems starting in childhood. Overall, males reported more impaired social functioning in adulthood than females. However, females with persistent high-level externalizing behaviour reported more impairment in relationships than males with persistent high-level externalizing behaviour. Conclusion. The long-term consequences of high levels of opposition and status violations in childhood to serious social problems during adulthood are much stronger than for individuals who show only high levels of aggressive antisocial behaviours. Copyright © 2007 Cambridge University Press

Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain

We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. We consider a (singular) perturbative expansion around this limit and study in particular how the non-topological field assume the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such phenomenon to arise in a quite large class of field-theoretical models.Comment: 18 pages, 2 figure

Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy

Time-resolved measurement techniques are opening a window on nonequilibrium quantum phenomena that is radically different from the traditional picture in the frequency domain. The simulation and interpretation of nonequilibrium dynamics is a conspicuous challenge for theory. This paper presents a novel approach to quantum many-body dynamics that is based on a Hamiltonian formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for reduced density matrices. These equations have an underlying symplectic structure, and we write them in the form of the classical Hamilton equations for canonically conjugate variables. Applying canonical perturbation theory or the Krylov-Bogoliubov averaging method to the resulting equations yields a systematic approximation scheme. The possibility of using memory-dependent functional approximations to close the Hamilton equations at a particular level of the hierarchy is discussed. The geometric structure of the equations gives rise to reduced geometric phases that are observable even for noncyclic evolutions of the many-body state. The formalism is applied to a finite Hubbard chain which undergoes a quench in on-site interaction energy U. Canonical perturbation theory, carried out to second order, fully captures the nontrivial real-time dynamics of the model, including resonance phenomena and the coupling of fast and slow variables.Comment: 17 pages, revise

The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure

Fetching marked items from an unsorted database in NMR ensemble computing

Searching a marked item or several marked items from an unsorted database is a very difficult mathematical problem. Using classical computer, it requires $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an algorithm that fetches marked items in an unsorted database directly. It requires only a single query. It can find a single marked item or multiple number of items.Comment: 4 pages and 1 figur

Psychometric properties of the revised Developmental Behaviour Checklist scales in Dutch children with intellectual disability

The present study assessed the reliability and validity of the revised scales of the Developmental Behaviour Checklist (DBC) in a Dutch sample of children with intellectual disability (ID). The psychometric properties of the parent and teacher versions of the DBC were assessed in various subsamples derived from a sample of 1057 Dutch children (age range = 6-18 years) with ID or borderline intellectual functioning. Good test-retest reliability was shown both for the parent and teacher versions. Moderate inter-parent agreement and high one-year stability was found for the scale scores. Construct validity was satisfactory, although limited by high informant variance. The DBC scales showed good criterion-related validity, as indicated by significant mean differences between referred and non-referred children, and between children with and without a corresponding DSM-IV diagnosis. The reliability and validity of the revised DBC scales are satisfactory, and the checklist is recommended for clinical and research purposes

Strong Coupling Theory of Two Level Atoms in Periodic Fields

We present a new convergent strong coupling expansion for two-level atoms in external periodic fields, free of secular terms. As a first application, we show that the coherent destruction of tunnelling is a third-order effect. We also present an exact treatment of the high-frequency region, and compare it with the theory of averaging. The qualitative frequency spectrum of the transition probability amplitude contains an effective Rabi frequency.Comment: 4 pages with 3 figure