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The derivation of Lorentz-covariant generalizations of Ohms law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor $chi^mu_ u$ relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohms law, we prove the validity of Ohms law in every inertial frame. We further use the universal relation between $chi^mu_ u$ and the microscopic conductivity tensor $sigma_{kell}$ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohms law.
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Drift-reduced MHD models are widely used to study magnetised plasma phenomena, in particular for magnetically confined fusion applications, as well as in solar and astrophysical research. This letter discusses the choice of Ohms law in these models, the resulting dispersion relations for the dynamics parallel to the magnetic field, and the implications for numerical simulations. We find that if electron pressure is included in Ohms law, then both electromagnetic and finite electron mass effects must also be included in order to obtain physical dispersion relations. A simple modification to the plasma vorticity is also found which improves handling of low density regions, of particular relevance to the simulation of the boundary region of magnetised plasmas.
The interaction of lasers with plasmas very often leads to nonlocal transport conditions, where the classical hydrodynamic model fails to describe important microscopic physics related to highly mobile particles. In this study we analyze and further propose a modification of the Albritton- Williams-Bernstein-Swartz collision operator Phys. Rev. Lett 57, 1887 (1986) for the nonlocal electron transport under conditions relevant to ICF. The electron distribution function provided by this modification exhibits some very desirable properties when compared to the full Fokker- Planck operator in the local diffusive regime, and also performs very well when benchmarked against Vlasov-Fokker-Planck and collisional PIC codes in the nonlocal transport regime, where we find that the effect of the electric field via the nonlocal Ohms law is an essential ingredient in order to capture the electron kinetics properly.
The work reported in arXiv:1311.5619v1 proposes to produce continuous-variable cluster states through relativistic motion of cavities. This proposal does not produce the states claimed by the authors. The states actually produced are in general not known to be useful for measurement-based quantum computation.
I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn few physical applications: dynamics and Lorentz transformation in gravitational fields, Doppler shift. A reference frame in event space is a smooth field of orthonormal bases. Every reference frame is equipped by anholonomic coordinates. Using anholonomic coordinates allows to find out relative speed of two observers and appropriate Lorentz transformation. Synchronization of a reference frame is an anholonomic time coordinate. Simple calculations show how synchronization influences time measurement in the vicinity of the Earth. Measurement of Doppler shift from the star orbiting the black hole helps to determine mass of the black hole. We call a manifold with torsion and nonmetricity the metrichyph affine manifold. The nonmetricity leads to a difference between the auto parallel line and the extreme line, and to a change in the expression of the Frenet transport and moving basis. The torsion leads to a change in the Killing equation. We also need to add a similar equation for the connection. The analysis of the Frenet transport leads to the concept of the Cartan transport and an introduction of the connection compatible with the metric tensor. The dynamics of a particle follows to the Cartan transport. We need additional physical constraints to make a nonmetricity observable. Learning how torsion influences on tidal force reveals similarity between tidal equation for geodesic and the Killing equation of second type.
In the present paper, we give a simple proof of the level density of fixed trace square ensemble.We derive the integral equation of the level density of fixed trace square ensemble.Then we analyze the asymptotic behavior of the level density.
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