Breathers as Metastable States for the Discrete NLS equation

We study metastable motions in weakly damped Hamiltonian systems. These are believed to inhibit the transport of energy through Hamiltonian, or nearly Hamiltonian, systems with many degrees of freedom. We investigate this question in a very simple model in which the breather solutions that are thought to be responsible for the metastable states can be computed perturbatively to an arbitrary order. Then, using a modulation hypothesis, we derive estimates for the rate at which the system drifts along this manifold of periodic orbits and verify the optimality of our estimates numerically.Comment: Corrected typos. Added Acknowledgmen

On some Gaussian Bernstein processes in RN and the periodic Ornstein-Uhlenbeck process

In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of arbitrary dimension N, whose initial and final conditions are positive measures. We concentrate primarily on the case where the elliptic part of the parabolic operator is related to the Hamiltonian of an isotropic system of quantum harmonic oscillators. In this situation there are many Gaussian processes of interest whose existence follows from our analysis, including N-dimensional stationary and non-stationary Ornstein-Uhlenbeck processes, as well as a Bernstein bridge which may be interpreted as a Markovian loop in a particular case. We also introduce a new class of stationary non-Markovian processes which we eventually relate to the N-dimensional periodic Ornstein-Uhlenbeck process, and which is generated by a one-parameter family of non-Markovian probability measures. In this case our construction requires an infinite hierarchy of pairs of forward-backward heat equations associated with the pure point spectrum of the elliptic part, rather than just one pair in the Markovian case. We finally stress the potential relevance of these new processes to statistical mechanics, the random evolution of loops and general pattern theory.Comment: Research articl

Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system

In the 70's Schelling introduced a multi-agent model to describe the segregation dynamics that may occur with individuals having only weak preferences for 'similar' neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city-lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a new variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socio-economic correlates.Comment: 10 pages, 7 figures, final version accepted for publication in PR

Panel Cointegration Testing in the Presence of Common Factors

Panel unit root and no-cointegration tests that rely on cross-sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has e.g. been shown by Banerjee, Marcellino and Osbat (2004, 2005) via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit root test using a common factor structure to model the cross-sectional dependence, but not much work has been done yet for panel no-cointegration tests. This paper proposes a model for panel no-cointegration using an unobserved common factor structure, following the work on Bai and Ng (2004) for panel unit roots. The model enables us to distinguish two important cases: (i) the case when the non-stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We study the asymptotic behavior of some existing, residual-based panel no-cointegration, as suggested by Kao (1999) and Pedroni (1999, 2004). Under the DGP used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than sqrt(N)T as for independent panels. We then examine the properties of residual-based tests for no-cointegration applied to defactored data from which the common factors and individual components have been extracted.econometrics;

Cross-Sectional Dependence Robust Block Bootstrap Panel Unit Root Tests

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectionaldependence including (but not exclusive to) the popular common factor framework. Weconsider block bootstrap versions of the group-mean Im, Pesaran, and Shin (2003) and thepooled Levin, Lin, and Chu (2002) unit root coefficient DF-tests for panel data, originallyproposed for a setting of no cross-sectional dependence beyond a common time effect. Thetests, suited for testing for unit roots in the observed data, can be easily implemented asno specification or estimation of the dependence structure is required. Asymptotic propertiesof the tests are derived for T going to infinity and N finite. Asymptotic validity of thebootstrap tests is established in very general settings, including the presence of commonfactors and even cointegration across units. Properties under the alternative hypothesisare also considered. In a Monte Carlo simulation, the bootstrap tests are found to haverejection frequencies that are much closer to nominal size than the rejection frequenciesfor the corresponding asymptotic tests. The power properties of the bootstrap tests appearto be similar to those of the asymptotic tests.Economics (Jel: A)

Many-body effects in magnetic inelastic electron tunneling spectroscopy

Magnetic inelastic electron tunneling spectroscopy (IETS) shows sharp increases in conductance when a new conductance channel associated to a change in magnetic structure is open. Typically, the magnetic moment carried by an adsorbate can be changed by collision with a tunneling electron; in this process the spin of the electron can flip or not. A previous one-electron theory [Phys. Rev. Lett. {\bf 103}, 176601 (2009)] successfully explained both the conductance thresholds and the magnitude of the conductance variation. The elastic spin flip of conduction electrons by a magnetic impurity leads to the well known Kondo effect. In the present work, we compare the theoretical predictions for inelastic magnetic tunneling obtained with a one-electron approach and with a many-body theory including Kondo-like phenomena. We apply our theories to a singlet-triplet transition model system that contains most of the characteristics revealed in magnetic IETS. We use two self-consistent treatments (non-crossing approximation and self-consistent ladder approximation). We show that, although the one-electron limit is properly recovered, new intrinsic many-body features appear. In particular, sharp peaks appear close to the inelastic thresholds; these are not localized exactly at thresholds and could influence the determination of magnetic structures from IETS experiments.Analysis of the evolution with temperature reveals that these many-body features involve an energy scale different from that of the usual Kondo peaks. Indeed, the many-body features perdure at temperatures much larger than the one given by the Kondo energy scale of the system.Comment: 10 pages and 6 figure