International Journal of Modern Physics B

An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the second-order direct and exchange perturbation terms calculated with Kohn–Sham orbitals and Kohn–Sham energies except that one of the two Coulomb interactions entering each term is replaced by an effective interaction which contains information about long-, intermediate-, and short-range correlations beyond second-order perturbation theory. Such an effective interaction can rigorously be defined for the correlation energy of the uniform electron liquid and is evaluated with high accuracy in order to apply to the orbital-dependent correlation energy functional. The coupling-constant-averaged spin-parallel and spin-antiparallel pair correlation functions are also evaluated with high accuracy for the electron liquid. The present orbital-dependent correlation energy functional with the effective interaction borrowed from the electron liquid is valid for tightly-binding electrons as well as for nearly-free electrons in marked contrast with the conventional local density approximation. There is a strong possibility that the present orbital-dependent correlation energy functional, if applied to the so-called strongly correlated electron systems, will produce the energy-band structure significantly different from that calculated only with the orbital-dependent exchange energy functional particularly in the neighborhood of the Fermi level or the energy gap. A detailed discussion, accompanied by an accurate calculation of the quasiparticle energy dispersion of the electron liquid, is given about the relationship between Kohn–Sham equations and Dyson equations in order to justify the application of Kohn–Sham equations to the band theory.

We report on the search for symmetries in the genetic code involving the medium rank simple Lie algebras and , in the context of the algebraic approach originally proposed by one of the present authors, which aims at explaining the degeneracies encountered in the genetic code as the result of a sequence of symmetry breakings that have occurred during its evolution.

Starting with a self-consistent mode-coupling theory, which was obtained via renormalized perturbation expansion and dynamic scaling ideas, we implement a high d (space dimension) expansion coupled with ∊-expansion. From the theory, which is finite for the Kolmogorov régime, we extract the ultraviolet and infrared poles by means of a double Laurent expansion. The Kolmogorov constant C is found to be C = (40d/27)^1/3 in the lowest contributing order of the high d expansion. This yields the value C = 1.64414 in three dimensions.

A new approach to the magnetic hysteresis loop and magnetization relaxation of molecule magnet, Mn₁₂, is presented. The method, so called "quasi-thermal equilibrium (QTE) + erase phase (EP)" (QTE + EP), leads the dissipation in state evolution. The method gives an method to approach an irreversible quantum dynamic tunnelling and time evolution of system and straightly leads the hysteresis loops. The QTE can work well for the double-well system and is able to be extended to the multi-wells quantum system. The EP is based on the physics of random interaction with the environment that results the phase de-coherence or say "re-initial" of the phase of quantum state during the time evolution. The stairs in the magnetic loops of Mn₁₂ we have obtained quantitatively show the quantum resonant tunnelling. The relaxation of magnetization from initial lowest state is calculated for different temperatures and well shows the exponential behavior. The theoretical results well agree with the experiments.