Related papers: Simple analyticity criteria for repulsive multi-bo…

We study a system in which the quantum dynamics of electrons depend on the particle density in their neighborhood. For any on-site repulsive interaction, we show that the exact two-body and three-body ground states are bound states. We also…

We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In…

Within the hyperspherical framework, the solution of the time-independent Schroedinger equation for a n-particle system is divided into two steps, the solution of a Schroedinger like equation in the hyperangular degrees of freedom and the…

This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the…

Subdiffusive motion takes place at a much slower timescale than diffusive motion. As a preliminary step to studying reaction-subdiffusion pulled fronts, we consider here the hyperbolic limit $(t,x) \to (t/\varepsilon, x/\varepsilon)$ of an…

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…

We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a {\it unitary graph} in which the vertices represent distinguishable particles and the edges…

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 provide an explicit bound on the number of periodic points of a rational function defined over a number field, where the bound depends only on the number of primes of bad reduction and the degree of the function, and is linear in the…

Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…

We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an…

We investigate the problem of $N$ identical bosons that are coupled to an impurity particle with infinite mass. For non-interacting bosons, we show that a dynamical impurity-boson interaction, mediated by a closed-channel dimer, can induce…

We prove lower bounds for energy in the Gaussian core model, in which point particles interact via a Gaussian potential. Under the potential function $t \mapsto e^{-\alpha t^2}$ with $0 < \alpha < 4\pi/e$, we show that no point…

A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum…

In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has…

We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as…

Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroups $H$ of $G$. This is the main ingredient for proving that $P$…

In this paper we study the Martin boundary at infinity for a large class of purely discontinuous Feller processes on metric measure spaces. We show that if $\infty$ is accessible from an open set $D$, then there is only one Martin boundary…

We improve the best known upper bounds on the number of Ruelle resonances in disks of large radius for Gevrey uniformly hyperbolic flows. The proof is based on Rugh's approach of dynamical determinants that replaces the study of the flow…