Wigner function with correlation damping

We examine the effect of the decoherence-induced reduction of correlation length on a one-dimensional scattering problem by solving numerically the evolution equation for the Wigner function with decoherence proposed by Barletti et al. [J. Comput. Theor. Transp. 47, 209 (2018)]. The numerical solution is achieved by the splitting-scheme algorithm, suitably modified to include the decoherence term. Three cases are examined, corresponding to a reflection-dominated regime, a transmission-dominated regime, and an intermediate one. The dynamic evolution of the Wigner function is followed until the separation process of the reflected and of the transmitted packets is complete and it is observed for three different values of the correlation length. The outcomes show a broadening and flattening of the Wigner function which becomes progressively more pronounced as the correlation length is decreased. This results in a reduced reflection at low energies and in a reduced transmission at high energies

JVLA 1.5GHz continuum observation of CLASH clusters I: radio properties of the BCGs

We present high-resolution ($\sim 1"$), 1.5 GHz continuum observations of the brightest cluster galaxies (BCGs) of 13 CLASH (Cluster Lensing And Supernova survey with Hubble) clusters at $0.18<z<0.69$ with the Karl G. Jansky Very Large Array (JVLA). Radio emission is clearly detected and characterized for 11 BCGs, while for two of them we obtain only upper limits to their radio flux ($<0.1$ mJy at 5$\sigma$ confidence level). We also consider five additional clusters whose BCG is detected in FIRST or NVSS. We find radio powers in the range from $2\times 10^{23}$ to $\sim 10^{26}$ $W~Hz^{-1}$ and radio spectral indices $\alpha_{1.5}^{30}$ (defined as the slope between 1.5 and 30 GHz) distributed from $\sim -1$ to $-0.25$ around the central value $\langle \alpha \rangle= - 0.68$. The radio emission from the BCGs is resolved in three cases (Abell 383, MACS J1931, and RX J2129), and unresolved or marginally resolved in the remaining eight cases observed with JVLA. In all the cases the BCGs are consistent with being powered by active galactic nuclei (AGN). The radio power shows a positive correlation with the BCG star formation rate, and a negative correlation with the central entropy of the surrounding intracluster medium (ICM) except in two cases (MACS J1206 and CL J1226). Finally, over the restricted range in radio power sampled by the CLASH BCGs, we observe a significant scatter between the radio power and the average mechanical power stored in the ICM cavities.Comment: 19 pages, 11 figures, significantly improved following referee's comments. Accepted by Ap