Related papers: Continuum percolation expressed in terms of densit…

We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…

We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…

We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…

For N impenetrable particles in one dimension where only the nearest and next-to-nearest neighbours interact, we obtain the complete spectrum both on a line and on a circle. Further, we establish a mapping between these N-body problems and…

The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of…

It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…

We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which…

We consider pairing in a dilute system of Fermions with a short-range interaction. While the theory is ill-defined for a contact interaction, the BCS equations can be solved in the leading order of low-energy effective field theory. The…

In this work we theoretically study pairing in two-dimensional Fermi gases, a system which is experimentally accessible using cold atoms. We start by deriving the mean-field pairing gap equation for a coordinate-space potential with a…

We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For…

Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that $N$-body systems with two-body zero-range interactions can be treated reliably and efficiently by the…

In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…

Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which…

The density-density correlations of the non-interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and…

This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…

We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…

We obtain the exact ground state and a part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in a case where N particles are interacting via nearest- and next-to-nearest neighbour interactions.…

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first…

For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for…