In this paper, we study non-interacting bosons in a quasi-disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic quasi-disorder produced by an Aubry–André potential. Using exact diagonalization, we investigate both the zero temperature and...

We present a theoretical study of the effects of the next-nearest-neighbor (NNN) hopping (t2) on the properties of non-interacting bosons in optical lattices in the presence of an Aubry–André quasi-disorder. First we investigate, employing exact diagonalization, the effects of t2 on the...

The PGBM model for a couple of counteracting, exponentially growing capital flows is presented: the available capital stock $X(t)$ evolves according to a variant of inhomogeneous geometric Brownian motion (GBM) with time-dependent drift, in particular, to the stochastic differential equation...

We studied the ferromagnetic Ising model on two-dimensional systems with rough boundaries and several thickness distributions. First, we considered very long strips with discretized Gaussian distributions of widths with mean 3⩽L⩽12. Systems with fixed interface width W and with increasing...

The power series coherent anomaly method is applied to study the critical properties of a classical Heisenberg model. The values of true critical temperature Tc∗ are obtained. Using these results the estimation of critical exponent γ for the zero-field static susceptibility has been made. The...

Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion...

The application of renormalization group (RG) theory to the asymptotic analysis of differential equations is considered. It is found that there is a class of small structural perturbations whose effects cannot be systematically treated using the Gell-Mann–Low RG approach applied in this...

We use the Migdal–Kadanoff renormalization group technique to study the spin-3/2 Blume–Capel model under a random crystal field, in the two- and three-dimensional cases. Studying the fixed points and the phase diagrams established, we find interesting results allowing us to understand the...

In this paper, we study the multicritical behavior of the Ginzburg–Landau model in a O(n1)⊕O(n2)-symmetric version containing (n1/2+n2/2)-complex order parameters coupled to a gauge field. We develop the RG analysis at a one-loop approximation in the context of the ϵ-expansion approach. The...

We study the critical temperatures obtained from the Migdal-Kadanoff (MK) renormalization transformation scheme for various ferromagnetic and frustrated Ising systems. We point out various problems in previous arguments and methods for obtaining the ordering temperatures for spin glasses using...