Related papers: Exact solution of Calogero model with competing lo…
An exposition of the different definitions and approaches to quantum statistics is given, with emphasis in one-dimensional situations. Permutation statistics, scattering statistics and exclusion statistics are analyzed. The Calogero model,…
Recently a partially solvable many-body problem with nearest and next-nearest neighbour interactions is proposed [cond-mat/9904121]. We show that by adding a suitably chosen momentum dependent nearest neighbour interaction, such a model can…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
This paper studies convergence to equilibrium for second-order Langevin dynamics under general growth conditions on the potential. Although we are principally motivated by the case when the potential is singular, e.g. when the dynamics has…
We analyze theoretically the effects of excluded-volume interactions between motors on the dynamics of a cargo driven by multiple motors. The model considered shares many commons with other recently proposed in the literature, with the…
In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general $n$-dimensional deformation of the two-center problem by adding arbitrary functions supporting second order commuting conserved…
The Calogero model with external harmonic oscillator potential is discussed from sL(2,R) algebra point of view. Explicit formulae for functions with exponential time behaviour are given; in particular, the integrals of motion are…
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the…
We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1,1) structure of the model. We show how SU(1,1)…
Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…
We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate…
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
This paper presents existence and uniqueness results for a propagative model of simultaneous impacts that is guaranteed to conserve energy and momentum in the case of elastic impacts with extensions to perfectly plastic and inelastic…
Most theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence these studies have been focused on the electrolyte structure around an isolated central particle (or elctrode), where…
Models that remain integrable even in confining potentials are extremely rare and almost non-existent. Here, we consider a one-dimensional hyperbolic interaction model, which we call as the Hyperbolic Calogero (HC) model. This is…
The theoretical description of the interplay between coherent evolution and chemical exchange, originally developed for magnetic resonance and later applied to other spectroscopic regimes, was derived under incorrect statistical…
We study a class of random matrices arising from the Lax matrix structure of classical integrable systems, particularly the Calogero family of models. Our focus is the density of eigenvalues for these random matrices. The problem can be…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…
The self-avoid random walk algorithm has been extensively used in the study of polymers. In this work we study the basic properties of the trajectories generated with this algorithm when two interactions are added to it: contact and folding…