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The current understanding of some important nonlinear collective processes inquantum plasmas with degenerate electrons is presented. After reviewing thebasic properties of quantum plasmas, we present model equations (e.g. thequantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations)that describe collective nonlinear phenomena at nanoscales. The effects of theelectron degeneracy arise due to Heisenberg's uncertainty principle and Pauli'sexclusion principle for overlapping electron wavefunctions that result intunneling of electrons and the electron degeneracy pressure. Since electronsare Fermions (spin-1/2), there also appears an electron spin current and a spinforce acting on electrons due to the Bohr magnetization. The quantum effectsproduce new aspects of electrostatic (ES) and electromagnetic (EM) waves in aquantum plasma that are summarized in here. Furthermore, we discuss nonlinearfeatures of ES ion waves and electron plasma oscillations (ESOs), as well asthe trapping of intense EM waves in quantum electron density cavities.Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS)and Poisson equations reveal the formation and dynamics of localized ESstructures at nanoscales in a quantum plasma. We also discuss the effect of anexternal magnetic field on the plasma wave spectra and develop quantummagnetohydrodynamic (Q-MHD) equations. The results are useful for understandingnumerous collective phenomena in quantum plasmas, such as those in compactastrophysical objects, in plasma-assisted nanotechnology, and in thenext-generation of intense laser-solid density plasma interaction experiments.

Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids