Related papers: The Existence of Pair Potential Corresponding to S…
It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points in $\mathbb{R}^d$). In this paper we…
We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large $\beta$). The main results are bounds on percolation thresholds…
We define a potential-weighted connective constant that measures the effective strength of a repulsive pair potential of a Gibbs point process modulated by the geometry of the underlying space. We then show that this definition leads to…
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
Given a classical gas described by the truncated correlation functions of all orders, we prove convergence of an expansion of the pair interaction part of the (unknown) potential in terms of the truncated correlation functions of all…
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…
The Kirkwood superposition is a well-known tool in statistical physics to approximate the $n$-point correlation functions for $n\geq 3$ in terms of the density $\rho $ and the radial distribution function $g$ of the underlying system.…
A contact potential describing an effective interaction between atomic $^4$He reproducing the results obtained with the HFDHE2 potential by Aziz et al. is employed to study the resulting equation of state by means of Quantum Monte Carlo…
In this article it is shown that in an equilibrium classical canonical ensemble of molecules with two-body interaction and external field full Gibbs distribution can be uniquely expressed in terms of a reduced two-particle distribution…
Many liquids have curves (isomorphs) in their phase diagrams along which structure, dynamics, and some thermodynamic quantities are invariant in reduced units. A substantial part of their phase diagrams is thus effectively one dimensional.…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's…
A method from random-matrix theory is used to calculate the pair correlation function of a one-dimensional gas of $N\gg 1$ classical particles with a power law repulsive interaction potential $u(x)\propto |x|^{-s}$ (a socalled Riesz gas).…
There are various situations in which it is natural to ask whether a given collection of $k$ functions, $\rho_j(\r_1,...,\r_j)$, $j=1,...,k$, defined on a set $X$, are the first $k$ correlation functions of a point process on $X$. Here we…
Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this…
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…
We study a classical lattice dipole gas with low activity in dimension $d \geq 3$. We investigate long distance properties by a renormalization group analysis. We prove that various correlation functions have an infinite volume limit. We…
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called potentials; equivalently, potentials can be defined as a…
We prove that the grand canonical Gibbs state of an interacting two-dimensional quantum Bose gas confined by a trapping potential converges to the complex Euclidean field theory with local quartic self-interaction, when the density of the…
Based on the relationship that the interaction energy between any two subsystems is equal to their internal energy multiplied by the interaction coefficient, we have derived a series correlated expressions of statistical physical…