Related papers: An inversion formula for the 2-body interaction gi…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…
A two-component four-fermion system with equal masses, interspecies s-wave scattering length a and vanishing intraspecies interactions under external spherically symmetric harmonic confinement is considered. Using a correlated Gaussian…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
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…
We prove a Gamma-convergence result for an energy functional related to some fractional powers of the Laplacian operator, with two singular perturbations (one in the interior and one on the boundary).
Previous functional integral methods for translationally invariant systems have been extended to the case of a confining trap potential. Essentially all finite-temperature properties of the repulsive Bose gas in a paraboloidal trap can be…
We review some recent progress on applications of Cluster Expansions. We focus on a system of classical particles living in a continuous medium and interacting via a stable and tempered pair potential. We review the cluster expansion in…
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The…
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…
We study the convergence of cluster and virial expansions for systems of particles subject to positive two-body interactions. Our results strengthen and generalize existing lower bounds on the radii of convergence and on the value of the…
We consider a dilute gas in 3D composed of two species of bosons interacting through positive inter-species and intra-species pairwise potentials. We prove a second order expansion for the energy density in the thermodynamic limit. For the…
The inverse Henderson problem of statistical mechanics concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction…
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…
The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the…
The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain $n$-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method…
We introduce a general physical formulation that allows one to obtain uniquely the effectiveinteractions by contracting the bare forces, even in highly concentrated systems. We tested it bystudying depletion forces in two-dimensional binary…
We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our…
From the principle of maximum entropy for a closed system in thermal equilibrium, for the first instance a clear relation is shown to exist between total entropy S (in terms of arrangements of particles) and the classical expression for the…
In this third paper of a series that started with arXiv:2106.10032 [math-ph] and continued with arXiv:2108.02659 [math-ph] we show that in $d\geq 3$ dimensions at low temperatures or high densities bosons interacting via pair potentials…