Elimination of the light shift in rubidium gas cell frequency standards using pulsed optical pumping

Changes in the intensity of the light source in an optically pumped, rubidium, gas cell frequency standard can produce corresponding frequency shifts, with possible adverse effects on the long-term frequency stability. A pulsed optical pumping apparatus was constructed with the intent of investigating the frequency stability in the absence of light shifts. Contrary to original expectations, a small residual frequency shift due to changes in light intensity was experimentally observed. Evidence is given which indicates that this is not a true light-shift effect. Preliminary measurements of the frequency stability of this apparatus, with this small residual pseudo light shift present, are presented. It is shown that this pseudo light shift can be eliminated by using a more homogeneous C-field. This is consistent with the idea that the pseudo light shift is due to inhomogeneity in the physics package (position-shift effect)

Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.Comment: 24 page

Systematic Investigation of Possibilities for New Physics Effects in b --> s Penguin Processes

Although recent experimental results in b-->s penguin process seem to be roughly consistent with the standard model predictions, there may be still large possibilities of new physics hiding in this processes. Therefore, here we investigate systematically the potential new physics effects that may appear in time-dependent CP asymmetries of B --> phi K^0, B--> eta^\prime K^0 and B--> K^0 \pi^0 decay modes, by classifying the cases for the values of the mixing-induced indirect CP asymmetries, S_{phi K^0}, S_{eta^\prime K^0}, S_{K^0 pi^0} which are compared to S_{J/psi K^0}. We also show that several B_s decay modes may help to resolve the ambiguities in such an analysis. Through combining analysis with the time-dependent CP asymmetries of B_s decay modes such as B_s --> phi eta^\prime, B_s--> eta^\prime pi^0 and B_s --> K^0 bar{K}^0, we can determine where the new CP phases precisely come from.Comment: 17 pages, version to be published in Prog.Theor.Phy

Structure of Stochastic Dynamics near Fixed Points

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition, but might have instead a divergence-free probability current. In the linear case the force can be split into two parts, one of which gives detailed balance with the diffusive motion, while the other induces cyclic motion on surfaces of constant cost function. Using the Jordan transformation for the force matrix, we find an explicit construction of the cost function. We discuss singularities of the transformation and their consequences for the stationary distribution. This Boltzmann-like distribution may be not unique, and nonlinear effects and boundary conditions may change the distribution and induce additional currents even in the neighborhood of a fixed point.Comment: 7 page