Related papers: Role of range of interactions in a model of diffus…
In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially…
We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice…
Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with…
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time…
With the recent production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models for…
It is common in the study of a dizzying array of soft matter systems to perform agent-based simulations of particles interacting via conservative and often short-ranged forces. In this context, well-established algorithms for efficiently…
We develop a theory describing neutral atoms scattering at low energies in an optical lattice. We show that for a repulsive interaction, as the microscopic scattering length increases, the effective scattering amplitude approaches a…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
The critical behavior of the non-diffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the…
We calculate an analytical expression for the terrace-width distribution $P(s)$ for an interacting step system with nearest and next nearest neighbor interactions. Our model is derived by mapping the step system onto a statistically…
It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbor interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different…
We study dynamical properties of the one- and two-dimensional Falicov-Kimball model using lattice Monte Carlo simulations. In particular, we calculate the spreading of charge correlations in the equilibrium model and after an interaction…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme.…
Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by…
Quantum simulators of lattice gauge theories involve dynamics of typically short-ranged interacting particles and dynamical fields. Elimination of the latter via Gauss law leads to infinite range interactions as exemplified by the Schwinger…
The present paper is devoted to the study of a simple model of interacting electrons in a random background. In a large interval $\Lambda$, we consider $n$ one dimensional particles whose evolution is driven by the Luttinger-Sy model, i.e.,…
A model of interacting one--dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first…