Extra dimensions and atomic transition frequencies

New unification theories predict large extra dimensions （LEDs）. If that is the case, gravity would be stronger at short ranges than what Newtonian gravity predicts. LEDs could also have effects at atomic level. In this paper we propose a new method to constrain the size of ‘gravity-only’ LEDs by analysing how these LEDs modify the energy of the atomic transitions 1s-2s and 2s-2p （Lamb shift）, in the particular case of the hydrogen and muonium atoms. We estimate these effects by using Bethe＇s non-relativistic treatment of Lamb shift. In the particular case of three LEDs, which may be a candidate to explain the interaction mechanism of dark matter particles, we have found that current knowledge in atomic spectroscopy could constrain their sizes to less than 10 μm. Although our contributions do not reach the sensitivity given by SN1987a, they are still slightly better than recent constraints given by Inverse Square Law tests of the Eoet-Wash group at Washington University, which gave R3 〈 36.6 μm.

Spatial Localization for Nonlinear Dynamical Stochastic Models for Excitable Media

Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.