Current relativistic

Plasma Radiolysis of CO2 Provided by High-Current Relativistic Electron Beams... 

Fridman, A. (1976b), Water Vapor Decomposition in Non-Self-Sustained Atmospheric Pressure Glow Discharge Supported by High-Current Relativistic Electron Beam, M.S. Dissertation, Moscow Institute of Physics and Technology, Moscow. 

Current relativistic electronic structure theory is now in a mature and well-developed state. We are in possession of sufficiently detailed knowledge on relativistic approximations and relativistic Hamiltonian operators which will be demonstrated in the course of this book. Once a relativistic Hamiltonian has been chosen, the electronic wave function can be constructed using methods well known from nonrelativistic quantum chemistry, and the calculation of molecular properties can be performed in close analogy to the standard nonrelativistic framework. In addition, the derivation and efficient implementation of quantum chemical methods based on (quasi-)relativistic Hamiltonians have facilitated a very large amount of computational studies in heavy element chemistry over the last two decades. Relativistic effects are now well understood, and many problems in contemporary relativistic quantum chemistry are technical rather than fundamental in nature. 

This chapter provides only a brief discussion of relativistic calculations. Currently, there is a small body of references on these calculations in the computational chemistry literature, with relativistic core potentials comprising the largest percentage of that work. However, the topic is important both because it is essential for very heavy elements and such calculations can be expected to become more prevalent if the trend of increasing accuracy continues. 

Relativistic methods can be extended to include electron correlation by methods analogous to those for the non-relativistic cases, e.g. Cl, MCSCF, MP and CC. Such methods are currently at the development stage. ... 

In summary, a fully relativistic theoretical description of photo emission for magnetic solids has been presented that is based on multiple scattering theory. For the VB-XPS case a very simple expression for the photo current intensity is found that can... 

To a good approximation one can assume that there are two independent groups of electrons (or channels) which carry the current, majority (or spin up) and minority (or spin down). Relativistic effects can couple the electron s spin to its motion through the lattice, but this effect is usually small for the transition metals and has not been included in the calculations shown here. 

For both alloy systems the theoretical results for p obtained in a fully relativistic are found in very satisfying agreement with the corresponding experimental data. In addition to these calculations a second set of calculations has been done making use of the two-current model. This means the partial resistivities p have been calculated by performing scalar relativistic calculations for every spin subsystem separately. As can be seen, the resulting total isotropic resistivity p is reasonably close to the fully relativistic result. Furthermore, one notes that the relative deviation of both sets of theoretical data is more pronounced for Co2,Pdi 2, than for Co2,Pti 2,. This has to be... 

Figure 2 Residual isotropic resistivity p of disordered Co Pdi- (open symbol.s) and CoiPti i (full symbols) alloys. Theoretical results obtained in a fully relativistic way and using the two-current model are given by up and down-pointing triangles, re- spectively. All other symbols represent experimental data taken from various sources [13, 14, 15, 16].

How is physics, as it is currently practiced, deficient in its description of nature Certainly, as popularizations of physics frequently reniiiid us, theories such as Quantum Electrodynamics are successful to a reinarkiible degree in predicting the results of experiments. However, any reasonable measure of success requires that wc add the caveat, ...in the domain (or domains) for which the theory was developed. For example, classical Newtonian physics is perfectly correct in its description of slow-moving, macroscopic objects, but is fundamentally incorrect in its description of quantum and/or relativistic systems. 

P should also minimize distinction.s between conventionally distinct but atomic. primitives (such as space, mass, time, etc.). The vision is to take one more step along the metaphoric road remove jnan from the center of the universe —> remove all privileged frames of reference —> remove all absolutes —> remove all distinction between space and matter—r remove all distinction ( ) Start by eliminating the tacit assumption that whatever physics is self-organizing itself out of the soup of the current crop of physicists is the physics of this universe in short, go from a solipsistic phys-ics to a fundamentally relativistic physics, wherein even physics itself becomes a set (an infinite hierarchical set ) of self-consistent world-views rather than a prescribed set of exactly/uniquely prescribed laws operating independently of all observers. 

Besides these many cluster studies, it is currently not knovm at what approximate cluster size the metallic state is reached, or when the transition occurs to solid-statelike properties. As an example. Figure 4.17 shows the dependence of the ionization potential and electron affinity on the cluster size for the Group 11 metals. We see a typical odd-even oscillation for the open/closed shell cases. Note that the work-function for Au is still 2 eV below the ionization potential of AU24. Another interesting fact is that the Au ionization potentials are about 2 eV higher than the corresponding CUn and Ag values up to the bulk, which has been shown to be a relativistic effect [334]. A similar situation is found for the Group 11 cluster electron affinities [334]. 

In the relativistic version of DFT, the ground state energy of the system is a unique functional of the fermion four-current density, / (/-) ... 

The general relativistic Hohenberg-Kohn-Sham formalism, outlined above, contains the spin degrees of freedom in a complete form. Consequently, the spin and kinetic motion effects are not separable. Indeed, they are contained in the external potential term as one can see if such term is written using the orbital current... 

All solutions of this Hamiltonian are thereby electronic, whether they are of positive or negative energy and contrary to what is often stated in the literature. Positronic solutions are obtained by charge conjugation. From the expectation value of the Dirac Hamiltonian (23) and from consideration of the interaction Lagrangian (16) relativistic charge and current density are readily identified as... 

Difficulties develop if the thermometer is exposed to certain types of radiation. However, calculations indicate that under normal circumstances, these radiation fields raise the temperature by only about 10 °C, which is a quantity that is not detectable even with the most sensitive current-day instruments [4]. Similarly, we shall neglect relativistic corrections that develop at high velocities, for we do not encounter such situations in ordinary thermodynamic problems. 

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