International Journal of Modern Physics B

Colloidal suspensions are ubiquitous in nature. They also occur in many processes of industrial and technological interest. However, an understanding of the basic microscopic interactions and the rich phase behavior exhibited by colloidal suspensions is still lacking. In the present paper we give a short overview of the different statistical-mechanical approaches that have been proposed to account for the phase behavior and phase transitions occurring in systems made up of spherical colloidal particles immersed in a fluid matrix of structureless solvent particles. Effective interactions in these systems are seen to be invariably of a very short-ranged nature, and particular emphasis is put on different models that very accurately approximate these interactions. A central theme of this review is the effect of correctly incorporating the correlation structure of the colloidal system into the statistical-mechanical treatment, and how this feature very decisively affects the quality of the theoretical predictions for the colloid thermodynamics and phase behavior. Based on the importance of the correlation structure, theories relying on perturbative expressions are seen to fail to a higher or lesser extent when applied to systems of particles interacting via short-ranged potentials, and a critical discussion is provided on different proposals to overcome these difficulties. In particular, a recently proposed self-consistent nonperturbative theory is reviewed, and some of its more recent applications are shown.

A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

We apply a new interaction Hamiltonian (Ref. 1) to two-dimensional and one-dimensional structures. We have found that, for small values of the wavevector, the interaction energy presents a logarithmic divergence and in a one-dimensional lattice, a cotangent divergence in addition. But, in a two-dimensional lattice the divergence terms may cancel, and from the point of view of the interactions the crystal structure is possible. The interaction energy has a polynomial dependence on the form 1/aⁿ where the maximum value of n is 7; a is the lattice constant.

The problem of precise estimation of the low-lying discrete energy spectrum of quantum dots was addressed rigorously by means of the methods of upper and lower bounds for eigenvalues of linear Hermitian operators in Hilbert space. It was shown that the method of intermediate problems for eigenvalues and the classical Rayleigh–Ritz method may be fused into effective tool of analytical and numerical investigation of the energy spectrum of quantum dots thus enabling and facilitating calculation of eigenvalues with controlled or prescribed precision. As an example, the energy spectrum problem for a simple two-electron quantum dot with harmonic-oscillator spherical confinement potential was thoroughly analyzed. Precise numerical calculations corroborated that in the absence of external magnetic field the ground state of the dot is the spin singlet for quantum dots of arbitrary characteristic size, so that no spontaneous singlet-triplet "phase transition" can occur.

Nanostructural zinc oxide has been successfully fabricated by heating the mixture of ZnO and graphite powders in air. The growth of these zinc oxide nanostructures with respect to the growing time and temperature has been studied. The morphologies and the crystal structures have been characterized by scanning electronic microscopy and the X-ray diffraction. The results indicated that ZnO nanostructure formed mainly along the crystal orientation [002] on silicon substrate at moderate temperatures. The crystallization was improved by prolonging growth time and the morphologies mainly depended on the distribution of the growth temperature. The growth process was attributed to vapor-liquid-solid mechanism.

Based on the entangled state representation and the appropriate bosonic phase operator we develop the superconducting capacitor model in the presence of a voltage bias and a current bias. In so doing, the full Hamiltonian operator theory for a superconducting barrier is established.

In this work the variational Roth's approach previously developed by the present authors to describe cuprate systems is extended to include the superconducting properties. We extend the Beenen and Edwards approach by including the d–p hybridization. The role of the d–p hybridization in modifying the values of superconducting order parameter is then studied in terms of the adopted values of the parameters defining the Hamiltonian of the system.

The tubulin dimers of microtubules are arranged in a crystalline lattice which is wrapped to form a long cylinder. Two different arrangements of monomers within the lattice have been postulated: the A-lattice and the B-lattice. Previous studies have assumed that both lattice types are hexagonal with each dimer surrounded by six nearest-neighbors. Based on recent biochemical studies I argue that both lattice types can also be formed with each dimer having four nearest-neighbors. This has important consequences for the overall behavior of the model. It is generally assumed that tubulin dimers possess a mobile electric dipole which can exist in one of two discrete Ising spin states: -1 (down) or +1 (up). The average of all these states within a microtubule is the mean polarization and is a measure of the dipole ordering within the lattice. Microtubule models with six nearest-neighbors behave like models of ferroelectric substances: at low temperatures the lattice is highly ordered with most (if not all) dipoles pointing in the same direction, but as the temperature increases, the degree of ordering decreases due to random thermal flipping of the dipoles. The mean polarization is particularly erratic at physiological temperatures. In contrast, when the microtubule lattice is modeled with four nearest-neighbors, the mean lattice polarization is quite stable and remains close to zero over a wide temperature range that includes 37°C (310K). This raises new questions about the biophysical role of microtubules.

We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin–spin couplings are the same in both directions. The exact correlation functions can be obtained by D log Padé for the cases with simple algebraic resultant expressions. The present results show that when the two spins are infinitely far from each other, the correlation function is equal to the product of the row magnetizations of the corresponding spins, as expected. In terms of low-temperature series expansions, the approach of this mth row correlation function to the bulk correlation function for increasing m can be understood from the observation that the dominant terms of their series expansions are the same successively in the above two correlation functions. The number of these dominant terms increases monotonically as m increases.