Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics. The theorem shows that essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a single experimental arrangement. Moreover, the predictions by those theories must significantly differ from those by quantum mechanics. Experimental results evidently refute the theorem's predictions for these theories and favour those of quantum mechanics. The conclusions are philosophically startling: either one must totally abandon the realistic philosophy of most working scientists, or dramatically revise out concept of space-time.

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Bell's theorem. Experimental tests and implications

Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects (e.g., the interior of white dwarf stars, in magnetars, etc.), in semiconductors and micromechanical systems, as well as in the next-generation intense laser–solid density plasma interaction experiments and in quantum X-ray free-electron lasers. In contrast to classical plasmas, quantum plasmas have extremely high plasma number densities and low temperatures. Quantum plasmas are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, and holes) obey the Fermi–Dirac statistics. In quantum plasmas, 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 angular momentum spin. Inclusion of these quantum forces allows the existence of very high-frequency dispersive electrostatic and electromagnetic waves (e.g., in the hard X-ray and gamma-ray regimes) with extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave–wave and wave–electron interactions in dense quantum plasmas. Specifically, we focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of three-dimensional quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase-space kinetic structures and mechanisms that can generate quasistationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed. Finally, future perspectives of the nonlinear quantum plasma physics are highlighted.

http://iopscience.iop.org/article/10.3367/UFNe.0180.201001b.0055/pdf

Nonlinear aspects of quantum plasma physics

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, model equations (e.g., the quantum hydrodynamic and effective nonlinear Schrodinger-Poisson equations) are presented that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg’s uncertainty principle and Pauli’s exclusion principle for overlapping electron wave functions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2 quantum particles), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, nonlinear features of ES ion waves and electron plasma oscillations are discussed, as well as the trapping of intense EM waves in quantum electron-density cavities. Specifically, simulation studies of the coupled nonlinear Schrodinger and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. The effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic equations are also discussed. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets), as well as in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, nanophotonics and nanoplasmonics, metallic nanostructures, thin metal films, semiconductor quantum wells, and quantum dots, etc.), and in the next generation of intense laser-solid density plasma interaction experiments relevant for fast ignition in inertial confinement fusion schemes.

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

Several recent astrophysical observations of distant type Ia supernovae have revealed that the content of the universe is made of about 70% of dark energy, 25% of dark matter and 5% of baryonic (visible) matter [1]. Thus, the overwhelming preponderance of matter and energy in the universe is believed to be dark i.e. unobservable by telescopes. The dark energy is responsible for the accelerated expansion of the universe. Its origin is mysterious and presumably related to the cosmological constant. Dark energy is usually interpreted as a vacuum energy and it behaves like a fluid with negative pressure. Dark matter also is mysterious. The suggestion that dark matter may constitute a large part of the universe was raised by Zwicky [2] in 1933. Using the virial theorem to infer the average mass of galaxies within the Coma cluster, he obtained a value much larger than the mass of luminous material. He realized therefore that some mass was “missing” in order to account for observations. This missing mass problem was confirmed later by accurate measurements of rotation curves of disc galaxies [3, 4]. The rotation curves of neutral hydrogen clouds in spiral galaxies measured from the Doppler effect are found to be roughly flat (instead of Keplerian) with a typical rotational velocity v∞ ∼ 200km/s up to the maximum observed radius of about 50 kpc. This mass profile is much more extended than the distribution of starlight which typically converges within ∼ 10 kpc. This implies that galaxies are surrounded by an extended halo of dark matter whose mass M(r) = rv 2/G increases linearly with radius [56]. This can be conveniently modeled by an isothermal self-gravitating gas the density of which scales asymptotically as r −2 [6].

Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: I. Analytical results

Quantum-mechanical phase-space distributions, introduced by Wigner in 1932, provide an intuitive alternative to the usual wave-function approach to problems in scattering and reaction theory. The aim of the present work is to collect and extend previous efforts in a unified way, emphasizing the parallels among problems in ordinary quantum theory, nuclear physics, chemical physics, and quantum field theory. The method is especially useful in providing easy reductions to classical physics and kinetic regimes under suitable conditions. Section II, dealing in detail with potential scattering of a spinless nonrelativistic particle, provides the background for more complex problems. Following a brief description of the two-body problem, the authors address the N-body problem with special attention to hierarchy closures, Boltzmann-Vlasov equations, and hydrodynamic aspects. The final section sketches past and possibly future applications to a wide variety of problems.

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Quantum collision theory with phase-space distributions

Es wird gezeigt, das man die Schrodingersche Gleichung des Einelektronen-problems in die Form der hydrodynamischen Gleichungen transformieren kann.

E. Madelung

Papers

Quantentheorie in hydrodynamischer Form