Dynamical phase diagram of Gaussian BEC wave packets in optical lattices

We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the Discrete Nonlinear Schr\"odinger Equation (DNLS). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping and moving breathers. However, we find that the actual DNLS dynamics shows a completely different diagram than the variational prediction. We numerically calculate a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure which can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian

Convergence Rates of Gaussian ODE Filters

A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives \emph{a priori} as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. This article establishes worst-case local convergence rates of order $q+1$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyses how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we show that, in the globally convergent case, the posterior credible intervals are well calibrated in the sense that they globally contract at the same rate as the truncation error. We illustrate these theoretical results by numerical experiments which might indicate their generalizability to $q \in \{2,3,\dots\}$.Comment: 26 pages, 5 figure

Questioning the existence of a unique ground state structure for Si clusters

Density functional and quantum Monte Carlo calculations challenge the existence of a unique ground state structure for certain Si clusters. For Si clusters with more than a dozen atoms the lowest ten isomers are close in energy and for some clusters entropic effects can change the energetic ordering of the configurations. Isotope pure configurations with rotational symmetry and symmetric configurations containing one additional isotope are disfavored by these effects. Comparisons with experiment are thus difficult since a mixture of configurations is to be expected at thermal equilibrium

Fractal Conductance Fluctuations of Classical Origin

In mesoscopic systems conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system with either fully chaotic or mixed phase space generically exhibits fractal conductance fluctuations unrelated to quantum interference. This might explain the unexpected dependence of the fractal dimension of the conductance curves on the (quantum) phase breaking length observed in experiments on semiconductor quantum dots.Comment: 5 pages, 4 figures, to appear in PR

Does Twitter matter? The impact of microblogging word of mouth on consumers’ adoption of new movies

This research provides an empirical test of the “Twitter effect,” which postulates that microblogging word of mouth (MWOM) shared through Twitter and similar services affects early product adoption behaviors by immediately disseminating consumers’ post-purchase quality evaluations. This is a potentially crucial factor for the success of experiential media products and other products whose distribution strategy relies on a hyped release. Studying the four million MWOM messages sent via Twitter concerning 105 movies on their respective opening weekends, the authors find support for the Twitter effect and report evidence of a negativity bias. In a follow-up incident study of 600 Twitter users who decided not to see a movie based on negative MWOM, the authors shed additional light on the Twitter effect by investigating how consumers use MWOM information in their decision-making processes and describing MWOM’s defining characteristics. They use these insights to position MWOM in the word-of-mouth landscape, to identify future word-of-mouth research opportunities based on this conceptual positioning, and to develop managerial implications

Not all digital word of mouth is created equal: Understanding the respective impact of consumer reviews and microblogs on new product success

The expansion of the Internet and social media have triggered a differentiation of the word-of-mouth (WOM) concept, with consumer communication about brands and products now taking place in various settings and forms. Two important digital WOM types are microblogs and consumer reviews. To clarify their differential roles for product success, this study offers a theoretical framework of the influence of these two types of WOM, drawing from consumer information search theory and diffusion theory. The tests of the proposed framework use a longitudinal data set of video game sales and weekly information gathered from microblogs (i.e., over 13 million tweets from Twitter) and consumer reviews (i.e., more than 17,000 Amazon consumer reviews). Analyzing a system of equations provides evidence that the influence of microblogs and consumer reviews on new product success changes over time. Prior to launch, the volumes of microblogs and consumer reviews, together with advertising, represent primary sales drivers. After launch, the volume of microblogs is initially influential, then loses impact, whereas the impact of the volume of consumer reviews continues to grow. The valence of consumer reviews gains significance only near the end of the observation period, but the valence of microblogging is never influential

Self-organized escape of oscillator chains in nonlinear potentials

We present the noise free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values