On the weighted forward reduced Entropy of Ricci flow

In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing under Ricci flow. Moreover, we show that, just the same as the Perelman's reduced volume, the weighted reduced volume entropy has the value $(4\pi)^{\frac{n}{2}}$ if and only if the Ricci flow is the trivial flow on flat Euclidean space.Comment: 10 page

Yamabe flow and ADM Mass on asymptotically flat manifolds

In this paper, we investigate the behavior of ADM mass and Einstein-Hilbert functional under the Yamabe flow. Through studying the Yamabe flow by weighted spaces, we show that ADM mass and Einstein-Hilbert functional are well-defined and monotone non-increasing under the Yamabe flow on $n$-dimensional, $n\geq 3$, asymptotically flat manifolds. In the case of dimension $n=3$ or 4, we obtain that the ADM mass is invariant under the Yamabe flow and the Yamabe flow is the gradient flow of Einstein-Hilbert functional on asymptotically flat manifold

Observation of recoil-induced resonances and electromagnetically induced absorption of cold atoms in diffuse light

In this paper we report an experiment on the observation of the recoil-induced resonances (RIR) and electromagnetically induced absorption (EIA) of cold Rb87 atoms in diffuse light. The pump light of the RIR and the EIA comes from the diffuse light in an integrating sphere, which also serves the cooling light. The probe light beam is a weak laser split from the cooling laser in order to keep the cooling and probe lasers correlated. We measured the RIR and the EIA signal varying with the detuning of the diffuse laser light, and also measured the temperature of the cold atoms at the different detunings. The mechanism of RIR and EIA in the configuration with diffuse-light pumping and laser probing is discussed, and the difference of nonlinear spectra of cold atoms between in diffuse-light cooling system and in optical molasses as well as in a magneto-optical trap (MOT) are studied.Comment: 9 pages, 6 figure