Emerging possibilities for creating and studying novel plasma regimes, e.g. relativistic plasmas and dense systems, in a controlled laboratory environment also require new modeling tools for such systems. This motivates theoretical studies of the kinetic theory governing the dynamics of plasmas for which both relativistic and quantum effects occur simultaneously. Here, we investigate relativistic corrections to the Pauli Hamiltonian in the context of a scalar kinetic theory for spin-1/2 quantum plasmas. In particular, we formulate a quantum kinetic theory for the collective motion of electrons that takes into account effects such as spin-orbit coupling and Zitterbewegung. We discuss the implications and possible applications of our findings. Contents

The Lagrangian equations of motion for massive spinning test particles (tops) moving on a gravitational background using General Relativity are presented. The paths followed by tops are nongeodesic. An exact solution for the motion of tops on a Schwarzschild background which allows for superluminal propagation of tops is studied. It is shown that the solution becomes relevant for particles with small masses, such as neutrinos. This general result is used to calculate the necessary condition to produce superluminal motion in part of the trajectory of a small mass particle in a weak gravitational field. The condition for superluminal motion establishes a relation between the mass, energy and total angular momentum of the particle.

It is shown that a vorticity, constructed from spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that obeys the standard vortex dynamics. Expressions for the quantum or spin vorticity, and for the resulting generalized helicity invariant are derived. Reduction of the rather complex spinning quantum system to a well known and highly investigated classical form opens familiar channels for the delineation of physics peculiar to dense plasmas spanning solid state to astrophysical objects. A simple example is worked out to show that the magnetics of a spinning plasma can be much richer than that of the corresponding classical system. PACS numbers: 52.35. We, 67.25.dk, 67.30.hj Keywords: Quantum vorticity; spin quantum plasmas; conserved helicity.In this paper we demonstrate that a spinning quantum fluid plasma [1,2] retains the most interesting and defining features of a classical ideal fluid. We will show, in particular that it is possible to engineer a "grand generalized vorticity" (GGV) that obeys a vortex dynamic structure. Such a GGV is created by combining the erstwhile "generalized" classical vorticity Ω c = ∇ × P c , where P c = A + (mc/q)v is proportional to the canonical momentum [3,4], and a "quantum vorticity" Ω q constructed from the macroscopic spin vector field S.It is remarkable that we can rewrite a complex and physically rich system as a quantum spinning plasma as a standard vortex dynamics. At the very least it implies a new composite constant of motion (the grand generalized helicity) and the existence of an Alfven/Kelvin theorem. This formulation, however, has the potential for a far speedier extraction and exposition of a great many properties of spinning plasmas. The most important step in this new formulation is the construction/identification of the quantum vorticity vector Ω q . As we will see, the form for Ω q is, by no means, obvious. Before embarking on the technical formulation, it is pertinent to put the current work in a historical perspective.The "project" of the fluidization of quantum systems (Schrodinger, Pauli and Dirac equations) has been driven by two related but distinct objectives: 1) Earlier investigators [5][6][7][8], wishing to understand and interpret quantum mechanics in terms of familiar classical concepts, were content to devise appropriate fluid-like variables obeying the "expected" fluid like equations of motion: for example the continuity and the force balance equation. Quantum mechanics entered the latter through the so called "quantum forces" proportional to powers ofh. The fluidized system, of course, was equivalent to the original quantum one.2) After an extended hiatus following the initial studies * Electronic address: mahajan@mail.utexas.edu † Electronic address: faz@physics.utexas.edu in quantum plasmas [9][10][11][12][13], the impetus for the recent impressive comeback of the fluidization "project", however, has come from a ...

Based on the one-body particle-antiparticle Dirac theory of electrons, a set of relativistic quantum fluid equations for a spin half plasma is derived. The particle-antiparticle nature of the relativistic particles is explicit in this fluid theory, which also includes quantum effects such as spin. The nonrelativistic limit is shown to be in agreement with previous attempts to develop a spin plasma theory derived from the Pauli Hamiltonian. Harnessing the formalism to the study of electromagnetic mode propagation, conceptually new phenomena are revealed; the particle-antiparticle effects increase the fluid opacity to these waves, while the spin effects tend to make the fluid more transparent.Programa MECE Educacion Superior Fulbright CONICYT FONDECyT 1080658 1070854 Centro para el Desarrollo de la Nanociencia y la Nanotecnologia, CEDENN

We find exact solutions to Maxwell equations written in terms of four-vector potentials in nonrotating, as well as in Gödel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled second-order differential equations for combinations of the components of the four-vector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non-rotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gödel and Kerr spacetimes do not exhibit that behavior.

The magnetic reconnection process is studied in relativistic pair plasmas when the thermal and inertial properties of the magnetohydrodynamical fluid are included. We find that in both SweetParker and Petschek relativistic scenarios there is an increase of the reconnection rate owing to the thermal-inertial effects, both satisfying causality. To characterize the new effects we define a thermal-inertial number which is independent of the relativistic Lundquist number, implying that reconnection can be achieved even for vanishing resistivity as a result of only thermal-inertial effects. The current model has fundamental importance for relativistic collisionless reconnection, as it constitutes the simplest way to get reconnection rates faster than those accessible with the sole resistivity. Magnetic reconnection is a fundamental plasma process which is widely believed to play a key role in many phenomena occurring in laboratory, space and astrophysical plasmas. Most of the progress in the theory of magnetic reconnection has been done in the nonrelativistic regime [1,2]. However, in recent years it has been recognized the importance of reconnection processes in magnetically dominated environments, where special relativistic effects have to be considered [3,4]. Indeed, in these environments the magnetic energy density B 2 /8π largely exceeds the rest mass energy density mnc 2 , and thus the speed of the Alfvén wave v A = cB/(4πmnc 2 + B 2 ) 1/2 approaches the speed of light c. In particular, relativistic reconnection is extremely important in pair (electron-positron) plasmas such as those in pulsar magnetospheres [5,6], pulsar winds [7,8], soft gamma-ray repeaters [9,10], jets from gamma-ray bursts [11,12] and from active galactic nuclei [13,14].In spite of the fact that relativistic magnetic reconnection is becoming increasingly important in many aspects of modern astrophysics, only a few theoretical studies on the fundamental physics have been done. The problem of the relativistic generalization of the classical Sweet-Parker and Petschek reconnection models was approached for the first time by Blackman and Field [15], who argued that because of Lorentz contraction the inflow velocity of the reconnecting magnetic field is greatly enhanced and may approach to the speed of light. Their conclusion was confirmed by Lyutikov and Uzdensky [16] for the relativistic Sweet-Parker scenario. On the contrary, a subsequent analysis by Lyubarsky [17] showed that the reconnection inflow remains sub-relativistic in * Electronic address: luca.comisso@polito.it † Electronic address: felipe.asenjo@uai.cl both scenarios. These pioneer works were followed by a study of the relativistic Petschek-type shock with pressure anisotropy [18], and by resistive relativistic magnetohydrodynamic (RMHD) simulations which seemed to be more consistent with Lyubarsky's theory [19][20][21].It is important to point out that all previous theoretical models of relativistic reconnection were developed in the framework of resistive RMHD. However, collisionl...

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Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated to linear polarization) and dispersion. The particular case of a vacuum--dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times) while for earlier times it matches a Kasner Universe, is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is now dependent on light polarization and dispersion and its non-null geodesic behavior. New results presented here may help to tackle some issues related to the "horizon" problem.Comment: Accepted in Physical Review