4,544 research outputs found
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 and its first
derivatives \emph{a priori} as a Gauss--Markov process ,
which is then iteratively conditioned on information about . This
article establishes worst-case local convergence rates of order for a
wide range of versions of this Gaussian ODE filter, as well as global
convergence rates of order in the case of and an integrated Brownian
motion prior, and analyses how inaccurate information on coming from
approximate evaluations of 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 .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
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Does Twitter matter? The impact of microblogging word of mouth on consumersâ adoption of new movies
This research provides an empirical test of the âTwitter effect,â which postulates that microblogging word of mouth (MWOM) shared through Twitter and similar services affects early product adoption behaviors by immediately disseminating consumersâ 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 MWOMâs 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
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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
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