Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of N. N. Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics and condensed matter physics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach, and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem, in which the effect of all the other particles on any given particle is approximated by a single averaged effect, thus reducing a many-body problem to a single-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising and Heisenberg models, superconducting and superfluid systems, strongly correlated systems, etc. It seems likely that these technical advances in the many-body problem will be useful in suggesting new methods for treating and understanding many-particle interacting systems. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects, and for those who are interested in concrete applications.Comment: 60 pages, Refs.25

Reactions of C+ + Cl-, Br-, and I--A comparison of theory and experiment.

Rate constants for the reactions of C+ + Cl-, Br-, and I- were measured at 300 K using the variable electron and neutral density electron attachment mass spectrometry technique in a flowing afterglow Langmuir probe apparatus. Upper bounds of <10-8 cm3 s-1 were found for the reaction of C+ with Br- and I-, and a rate constant of 4.2 ± 1.1 × 10-9 cm3 s-1 was measured for the reaction with Cl-. The C+ + Cl- mutual neutralization reaction was studied theoretically from first principles, and a rate constant of 3.9 × 10-10 cm3 s-1, an order of magnitude smaller than experiment, was obtained with spin-orbit interactions included using a semiempirical model. The discrepancy between the measured and calculated rate constants could be explained by the fact that in the experiment, the total loss of C+ ions was measured, while the theoretical treatment did not include the associative ionization channel. The charge transfer was found to take place at small internuclear distances, and the spin-orbit interaction was found to have a minor effect on the rate constant

First-principles study of the polar O-terminated ZnO surface in thermodynamic equilibrium with oxygen and hydrogen

Using density-functional theory in combination with a thermodynamic formalism we calculate the relative stability of various structural models of the polar O-terminated (000-1)-O surface of ZnO. Model surfaces with different concentrations of oxygen vacancies and hydrogen adatoms are considered. Assuming that the surfaces are in thermodynamic equilibrium with an O2 and H2 gas phase we determine a phase diagram of the lowest-energy surface structures. For a wide range of temperatures and pressures we find that hydrogen will be adsorbed at the surface, preferentially with a coverage of 1/2 monolayer. At high temperatures and low pressures the hydrogen can be removed and a structure with 1/4 of the surface oxygen atoms missing becomes the most stable one. The clean, defect-free surface can only exist in an oxygen-rich environment with a very low hydrogen partial pressure. However, since we find that the dissociative adsorption of molecular hydrogen and water (if also the Zn-terminated surface is present) is energetically very preferable, it is very unlikely that a clean, defect-free (000-1)-O surface can be observed in experiment.Comment: 10 pages, 4 postscript figures. Uses REVTEX and epsf macro