Electronic surface states localized on the edge of a semi-infinite square lattice are studied in the tight binding approximation. We examined the existence of surface states in the presence of magnetic field applied in the surface region of a 2D lattice. The applied field is perpendicular to the lattice and confined to a stripe near the surface. We also included a surface site perturbation caused by the presence of the surface. The magnetic field is introduced into the model by the Peierls substitution.
Taking into account the full Coulomb potential and the excluded volume interactions, properties of dendrimers with generations g = 5, 6 with charged terminal groups and counterions in an athermal solvent are examined by lattice Monte Carlo simulations. The study treats counterions explicitly and focuses on the local structure of the systems inspected by pair correlation functions g_{ab} that provide information on distributions of monomers, terminal groups and ions in space at various temperatures T*. Special emphasis is placed on counterions and their role they play in causing conformational changes of the molecules. The simulations show that counterions penetrate the interior of the dendrimers, and there is a major increase in their concentration there as T* decreases. Some of them condense onto the terminal groups and a reduction in the mean effective charge ⟨Q⟩ of the dendrimers appears. Within the range of temperatures where the condensation (as a function of T*) is sharp the molecules weakly swell up when compared to their size at the other temperatures. This kind of behaviour is also reflected by the distributions of monomers and terminal groups.
Recently, on the basis of the Tsallis distribution of states the generalized Monte Carlo acceptance probabilities have been proposed and applied to various optimization problems. In the paper we used the generalized simulated annealing algorithms for the ±J spin glass model. Efficiency of the new annealing procedures was compared with that of the conventional methods. This was done with respect to the number of annealing steps and to the lowest energy found. The algorithms were applied to a system of 70×70 spins on a square lattice with periodical boundary conditions whose ground state configurations are known exactly. This enables us to evaluate the efficiency in a quantitative way.
Racah-Wigner type of calculus is adapted to the system of two free electrons in a cubic box, confined to a single star p00 of quasimomentum. Various coupling schemes (LS-like, jj-like, and transitive) have been reviewed in analogy to the case of a free atom. Racah recoupling matrices are calculated explicitly, and their quantum-mechanical meaning is exposed in terms of octahedral multipoles.
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