In this paper, we investigated the corrected plasmon dispersion relation for graphene in presence of a constant magnetic field which it includes a quantum term arising from the collective electron density wave interference effects. By using quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, the longitudinal plasmons ar...

Individuals collectively participate in all manner of endeavors including, for example, babysitting cooperatives, bowling leagues, and community associations. And yet failure to produce collective goods when they are desired is also widespread, such as when childcare or group leisure activities are unavailable, or communities pollute their local environment. Producing most collective goods enta...