Related papers: Homogenization of point interactions
We study the long-time behavior of scale-invariant solutions of the 2d Euler equation satisfying a discrete symmetry. We show that all scale-invariant solutions with bounded variation on $\mathbb{S}^1$ relax to states that are piece-wise…
We investigate gradient flows of some homogeneous functionals in R^N , arising in the Lagrangian approximation of systems of self-interacting and diffusing particles. We focus on the case of negative homogeneity. In the case of strong…
This article surveys results that relate homogenisation problems for partial differential equations and convergence in the weak operator topology of a suitable choice of linear operators. More precisely, well-known notions like…
The resolvent convergence of self-adjoint operators via the technique of $\Gamma$-convergence of quadratic forms is adapted to incorporate complex Hilbert spaces. As an application, we find effective operators to the Dirichlet Laplacian…
We study the homogeneous sector of the RST model describing the gravitational dynamics, including back-reaction, of radiating 2-d black holes. We find the exact solutions both in conformal gauge and in time-parametrized form, isolate the…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and…
Inspired by numerical studies of the aggregation equation, we study the effect of regularization on nonlocal interaction energies. We consider energies defined via a repulsive-attractive interaction kernel, regularized by convolution with a…
We study periodic homogenization by Gamma-convergence of some singular integral functionals related to nonlinear elasticity.
In this paper, we develop a general homogenization theory for elliptic equations with coefficients that oscillate periodically at infinitely many scales $\varepsilon = (\varepsilon_1, \varepsilon_2, \cdots) \in (0,1)^\infty$, with…
This chapter deals with the notion of the resolvent of a self-adjoint operator. We pay special attention to the convergence of unbounded self-adjoint operators in several resolvent senses, and how they are related to the convergence of…
Homogenization protocols model the quantum mechanical evolution of a system to a fixed state independently from its initial configuration by repeatedly coupling it with a collection of identical ancillas. Here we analyze these protocols…
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the…
We study discrete spectral quantities associated to Schr\"odinger operators of the form $-\Delta_{\mathbb{R}^d}+V_N$, $d$ odd. The potential $V_N$ models a highly disordered crystal; it varies randomly at scale $N^{-1} \ll 1$. We use…
The Hamiltonian of a pure hydrogen atom possesses the SO(4) symmetry group generated by the integrals of motion: the angular momentum and the Runge-Lenz vector. The pure hydrogen atom is a supersymmetric and superintegrable system, since…
Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic theories where the quasiparticles are distributed uniformly in space, and the equilibration involves only their velocity distribution. For such solutions, the…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
For real bounded functions \Phi and \Psi of compact support, we prove the norm resolvent convergence, as \epsilon and \nu tend to 0, of a family of one-dimensional Schroedinger operators on the line of the form S_{\epsilon, \nu}=…
A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…
We homogenize the Laplace and heat equations with the Neumann data oscillating in the ``vertical" $u$-variable. These are simplified models for interface motion in heterogeneous media, particularly capillary contact lines. The…