Finitude of physical measures for random maps

For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. We characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems. We also provide sufficient practical conditions for a random map to belong to these classes. For instance, we establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover Lebesgue almost all the manifold.Comment: 83 pages, 5 figure

Photo-disintegration cross section measurements on 186^{186}W, 187^{187}Re and 188^{188}Os: Implications for the Re-Os cosmochronology

Cross sections of the $^{186}$W, $^{187}$Re, $^{188}$Os($\gamma,n$) reactions were measured using quasi-monochromatic photon beams from laser Compton scattering (LCS) with average energies from 7.3 to 10.9 MeV. The results are compared with the predictions of Hauser-Feshbach statistical calculations using four different sets of input parameters. In addition, the inverse neutron capture cross sections were evaluated by constraining the model parameters, especially the $E1$ strength function, on the basis of the experimental data. The present experiment helps to further constrain the correction factor $F_{\sigma}$ for the neutron capture on the 9.75 keV state in $^{187}$Os. Implications of $F_{\sigma}$ to the Re-Os cosmochronology are discussed with a focus on the uncertainty in the estimate of the age of the Galaxy.Comment: 11 page

Polarization transfer in the 16^{16}O(p,p′)(p,p') reaction at forward angles and structure of the spin-dipole resonances

Cross sections and polarization transfer observables in the $^{16}$O$(p,p')$ reactions at 392 MeV were measured at several angles between $\theta_{lab}=$ 0$^\circ$ and 14$^\circ$. The non-spin-flip (${\Delta}S=0$) and spin-flip (${\Delta}S=1$) strengths in transitions to several discrete states and broad resonances in $^{16}$O were extracted using a model-independent method. The giant resonances in the energy region of $E_x=19-$27 MeV were found to be predominantly excited by ${\Delta}L=1$ transitions. The strength distribution of spin-dipole transitions with ${\Delta}S=1$ and ${\Delta}L=1$ were deduced. The obtained distribution was compared with a recent shell model calculation. Experimental results are reasonably explained by distorted-wave impulse approximation calculations with the shell model wave functions.Comment: 28 pages RevTex, including 9 figures, to be published in Phys. Rev. C.; a typo in Eq. (3b) was correcte

Near-threshold Lambda(1520) production by the gamma p -> K+Lambda(1520) reaction at forward K+ angles

Differential cross sections and photon-beam asymmetries for the gamma p -> K+ Lambda(1520) reaction have been measured with linearly polarized photon beams at energies from the threshold to 2.4 GeV at 0.6<cos(theta)<1. A new bump structure was found at W=2.11 GeV in the cross sections. The bump is not well reproduced by theoretical calculations introducing a nucleon resonance with J<=3/2. This result suggests that the bump might be produced by a nucleon resonance possibly with J>=5/2 or by a new reaction process, for example an interference effect with the phi photoproduction having a similar bump structure in the cross sections.Comment: 5 pages, 4 figures, published in Phys. Rev. Let

Measurement of the γ⃗p→K+Λ\vec{\gamma} p \to K^+ \Lambda Reaction at Backward Angles

Cross sections for the $\gamma p \to K^+ \Lambda$ have been measured at backward angles using linearly polarized photons in the range 1.50 to 2.37 GeV. In addition, the beam asymmetry for this reaction has been measured for the first time at backward angles. The $\Lambda$ was detected at forward angles in the LEPS spectrometer via its decay to $p\pi^-$ and the K^+ was inferred using the technique of missing mass. These measurements, corresponding to kaons at far backward angles in the center-of-mass frame, complement similar CLAS data at other angles. Comparison with theoretical models shows that the reactions in these kinematics provide further opportunities to investigate the reaction mechanisms of hadron dynamics.Comment: 6 figures, submitted to PRC rapid communication