International Journal of Modern Physics B

The concept of a spiral lattice is discussed. Some examples of known mineral structures, namely clino-asbestos, halloysite and cylindrite, are then interpreted in terms of this structural principle. An example of a synthetic sulphide catalyst spiral structure having atomic dimensions is also described. All of these inorganic spiral structures are based on the spiral of Archimedes. The principles for a new type of crystallography, based on the Archimedian spiral, are then presented.

Two quasiperiodic planar patterns with fivefold symmetry are derived from the root lattice A₄ in 4-space. A detailed analysis of the geometry of the A₄ Voronoi complex and its dual complex is presented with special emphasis on fivefold symmetry. By means of the general dualization method, 2D patterns are obtained, one with triangular tiles and a second which turns out to be the well-known Penrose pattern. The vertex configurations and their relative frequencies, the deflation rules, and the Fourier properties of these patterns are worked out in the framework of the dualization method and Klotz construction.

This paper reviews simulational and theoretical investigations of critical behavior in a stochastic, interacting lattice gas under the influence of a uniform external driving field. By studying this model system one wishes to gain a deeper understanding of steady states far from thermal equilibrium, and their dynamic universality classes. The major result in the case of attractive particle-particle interactions is the emergence of a novel non-equilibrium fixed point, different from the Wilson-Fisher fixed point of the equilibrium system. The fluctuations of internal energy, the structure factor and the two-point correlations all display surprising features associated with the non-equilibrium nature of the system. For repulsive interactions and small driving forces, one finds a continuous, Ising-like transition which turns first order for larger fields until it is completely destroyed.

The equation in the ladder approximation was derived for the two-particle Green function of the itinerant electrons with the Heisenberg ferromagnetic and antiferromagnetic interaction. The general form of its solution was found. The existence of the pole in this solution is related to the condensation of the bound pairs in the corresponding spin state. The condition for the pole determines the critical temperature T_c. The effective interaction between the mobile holes due to the mobile hole-localized spin coupling in the two-band Hubbard model was also studied.

In the frustrated Heisenberg model with first (J₁) and second (J₂) nearest neighbours interactions on a square lattice the transition from the long range order state (LROS) to spin liquid state (SLS) is found at α = J₁/J₂ ≅ 0.25. SLS is characterized by the gap in spin excitation spectrum at T = 0 and, hence, by exponential decay of spin correlation function at large distance. As a result, correlation length is temperature independent in SLS in accordance with neutron experiments on doped La₂CuO₄.

A two-mode boson system described by a Hamiltonian containing a nonlinear interaction of a general enough form is investigated. Nontrivial effects concerning a transition of a coherent state to a squeezed state and vice versa in the process of evolution of that system are revealed.

Exciton binding energy in semiconductor multiple quantum well (MQW) systems is analyzed with both the variational method and the perturbation theory. The intrinsic deficiency of the use of the two-dimensional exciton envelop wave function is clearly demonstrated. Using a GaAs/Al_xGa_1−xAs MQW as an example to calculate the exciton binding energy with a variational three-dimensional trial envelop function, we found that in many realistic samples the spatial extension of an exciton covers a region of several lattice constant d_A + d_B, where d_A is the barrier width and d_B is the well width.

The effective mass approximation (EMA), when applied to graded crystals, needs a modified form for the kinetic energy operator, where 2α + β = −1 and m(z) is the position-dependent effective mass. We have analyzed the energy dispersion of the EMA Hamiltonian, and performed a one-dimensional and a three-dimensional exact calculation to determine the proper value of β. Our conclusion is that when β = −1 the EMA provides better agreement with the exact solutions.

A solvable model of d = 1 spinless fermions at half-filling which exhibits a Mott transition is studied in detail. Many response functions are computed: at zero and nonzero temperatures, in the insulating and metallic sites, at the transition, and at q ≃ 0, 2k_F. Some quantities are computed exactly, others only upto a scale factor. Some results are old, but mentioned here for completeness. Some are rederived using new tools such as conformal invariance. The rest are new. Next, the effect of randomness on the Mott state is explored. It is found, on the basis of Imry-Ma type arguments that no matter how large the gap is, the Mott insulator turns into an Anderson insulator immediately.