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We have applied the gaussian auxiliary field method introduced by Mazenko to the ordering dynamics of a non-conserved scalar system with attractive long-range interactions. This study provides a test-bed for the approach and shows some of…
We develop a theoretical framework to determine distribution functions in nonequilibrium systems coupled to equilibrium reservoirs, by using the nonequilibrium Green's function technique. As a paradigmatic example, we consider the…
An alternative methodology to investigate indirect polyatomic processes with quasi-classical trajectories is proposed, which effectively avoids any binning or weighting procedure while provides rovibrational resolution. Initial classical…
We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce…
An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a…
The Poisson bipolar model considers user-base station pairs distributed at random on a flat domain, similar to matchsticks scattered onto a table. Though this is a simple and tractable setting in which to study dense networks, it doesn't…
We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of…
Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we…
Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid…
A mixture of spin-polarized light and heavy fermionic atoms on a finite size 2D optical lattice is considered at various temperatures and values of the coupling between the two atomic species. In the case, where the heavy atoms are immobile…
The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green's…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbour sites of the dice lattice accompanied by the…
We consider three problems for Gabor frames that have recently received much attention. The first problem concerns the approximation of dual Gabor frames in $L_2(R)$ by finite-dimensional methods. Utilizing Wexler-Raz type duality relations…
We consider 'supersaturation' problems in partially ordered sets (posets) of the following form. Given a finite poset $P$ and an integer $m$ greater than the cardinality of the largest antichain in $P$, what is the minimum number of…
Calculations of Drell-Yan (DY) production at next-to-leading (NLO) order have been combined with Transverse Momentum Dependent (TMD) distributions obtained with the Parton Branching (PB). The predictions show a remarkable agreement with DY…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
A series of III-V ternary and quarternary digital alloy avalanche photodiodes (APDs) have recently been seen to exhibit very low excess noise. Using band inversion of an environment-dependent atomistic tight binding description of short…
Ewens-Pitman's partition structure arises as a system of sampling consistent probability distributions on set partitions induced by the Pitman-Yor process. It is widely used in statistical applications, particularly in species sampling…
The iterative Boltzmann inversion is an iterative scheme to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function. Although the method is…