Related papers: Connected Coulomb Columns: Analysis and Numerics
The non-linear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology yet poses considerable challenge to achieve focused interactions on the…
We consider the problem of minimizing the Willmore energy connected surfaces with prescribed surface area which are confined to a finite container. To this end, we approximate the surface by a phase field function $u$ taking values close to…
We consider a multiple tunneling process into a quantum dot capacitively coupled to a dissipative environment. The problem is mapped onto an anisotropic Kondo model in its Coulomb gas representation. The tunneling barrier resistance and the…
We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience…
The one-- and two-- particle densities of up to four interacting electrons with spin, confined within a quasi one--dimensional ``quantum dot'' are calculated by numerical diagonalization. The transition from a dense homogeneous charge…
We consider the system of particles on a finite interval with pair-wise nearest neighbours interaction and external force. This model was introduced by Malyshev to study the flow of charged particles on a rigorous mathematical level. It is…
We establish phase transitions for continuum Delaunay multi-type particle systems (continuum Potts or Widom-Rowlinson models) with a repulsive interaction between particles of different types. Our interaction potential depends solely on the…
In this paper, we construct various examples of holomorphic laminations, with leaves of dimension 1, and we also study some of their dynamical properties. In particular we study existence and uniqueness of positive closed currents. We…
A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling, which we study on the continuum level by introducing a minimal coupling between…
In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface…
This paper concerns modeling of the evolution of intermittency region between two weakly miscible phases due to temporal and spatial variations of its characteristic length scale. First, the need of a more general description allowing for…
This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a non-local repulsive term. We characterize existence, non-existence and radial symmetry of the minimizers as a function of mass in the…
In one spatial dimension, quantum systems with an attractive three-body contact interaction exhibit a scale anomaly. In this work, we examine the few-body sector for up to six particles. We study those systems with a self-consistent,…
We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we…
We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We first present a Tomonaga-Luttinger liquid (TLL) description of the system.…
We study a variational model for a diblock-copolymer/homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove…
We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different…
We obtain the phase diagram of the double-exchange model at low electronic densities in the presence of electron-electron interactions. The single particle problem and its extension to low electronic densities, when a Wigner crystal of…
The competition between long-range and short-range interactions among holes moving in an antiferromagnet (AF), is studied within a model derived from the spin density wave picture of layered transition metal oxides. A novel numerical…
Studying the electronic structure of defects in materials is an important subject in condensed matter physics. From a mathematical point of view, nonlinear mean-field models of localized defects in insulators are well understood. We present…