相关论文: Next Order Asymptotics and Renormalized Energy for…
The paper deals with minimum energy problems in the presence of external fields with respect to the Riesz kernels $|x-y|^{\alpha-n}$, $0<\alpha<n$, on $\mathbb R^n$, $n\geqslant2$. For quite a general (not necessarily lower semicontinuous)…
We consider a system of $N$ bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normalized thickness of the box $d\ll1$. We assume particles to…
We establish, as $\rho\to 0$, an asymptotic expansion for the minimal Dirichlet energy of $\mathbb S^2$-valued maps outside a finite number of three-dimensional particles of size $\rho$ with fixed centers $x_j\in\mathbb{R}^3$, under general…
For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the…
We consider periodic energy problems in Euclidean space with a special emphasis on long-range potentials that cannot be defined through the usual infinite sum. One of our main results builds on more recent developments of Ewald summation to…
The regularized trace of the heat kernel of a one-dimensional Schr\"odinger operator with a singular two-particle contact interaction being of Lieb-Liniger type is considered. We derive a complete small-time asymptotic expansion in…
We consider two related problems: the first is the minimization of the "Coulomb renormalized energy" of Sandier-Serfaty, which corresponds to the total Coulomb interaction of point charges in a uniform neutralizing background (or rather…
The Hausdorff dimension of a set can be detected using the Riesz energy. Here, we consider situations where a sequence of points, $\{x_n\}$, ``fills in'' a set $E \subset \mathbb{R}^d$ in an appropriate sense and investigate the degree to…
A simple ansatz is suggested for the structure of threshold resummation of the momentum space physical evolution kernels (`physical anomalous dimensions') at all orders in (1-x), taking as examples Deep Inelastic Scattering (F_2(x, Q^2) and…
We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n…
Let $A$ be a compact $d$-rectifiable set embedded in Euclidean space $\RR^p$, $d\le p$. For a given continuous distribution $\sigma(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, our earlier results provided a method for…
We study the contact process with stirring on $\mathbb{Z}^d$. In this process, particles occupy vertices of $\mathbb{Z}^d$; each particle dies with rate 1 and generates a new particle at a randomly chosen neighboring vertex with rate…
We derive exact renormalization-group equations for the $n$-point vertices ($n=0,1,2,\cdots$) of interacting single-component Bose-Einstein condensates based on the vertex expansion of the effective action. They have a notable feature of…
We compute the equilibrium measure in dimension d=s+4 associated to a Riesz s-kernel interaction with an external field given by a power of the Euclidean norm. Our study reveals that the equilibrium measure can be a mixture of a continuous…
We describe a framework for extending the asymptotic behavior of a short-range interaction from the unit cube to general compact subsets of $ \mathbb R^d $. This framework allows us to give a unified treatment of asymptotics of…
The paper Brauchart, Hardin and Saff [Bull. Lond. Math. Soc. 41(4) (2009)] gives the complete asymptotic expansions of the Riesz $s$-energy of the $N$th roots of unity which form a universally optimal distribution of points on the unit…
We derive analytically the asymptotic behavior of the Casimir interaction between a sphere and a plate when the distance between them, $d$, is much smaller than the radius of the sphere, $R$. The leading order and next-to-leading order…
We investigate minimum weak $\alpha$-Riesz energy problems with external fields in both the unconstrained and constrained settings for generalized condensers $(A_1,A_2)$ such that the closures of $A_1$ and $A_2$ in $\mathbb R^n$ are allowed…
We propose to study the infrared behaviour of polymerised (or tethered) random manifolds of dimension D interacting via an exclusion condition with a fixed impurity in d-dimensional Euclidean space in which the manifold is embedded. We…
We consider the small separation asymptotic expansions of the Casimir interaction energy and the Casimir interaction force between two parallel cylinders. The leading order terms and the next-to-leading order terms are computed…