Nonlinear nanostructures in dense quantum plasmas

Abstract

Dense quantum plasmas are ubiquitous in compact astrophysical objects (e.g. the interior of white dwarf stars, in magnetars, etc.), in semiconductors and micro‐mechanical systems, as well as in the next generation intense laser‐solid density plasma interaction experiments. In contrast to classical plasmas, one encounters extremely high plasma density and low temperature in dense quantum plasmas. In the latter, the electrons and positrons obey the Fermi‐Dirac statistics, and there are new forces associated with i) quantum statistical electron and positron pressures, ii) electron and positron tunneling through the Bohm potential, and iii) electron and positron spin‐1/2. Inclusion of these quantum forces gives rise to very high‐frequency plasma waves (e.g. in the x‐ray regime) at nanoscales. Our objective here is to present nonlinear equations that depict the localization of electron plasma waves in the form of a quantum electron hole and quantum vortex, as well as the trapping of intense electromagnetic wav...