Related papers: Optimally Localized Wannier Functions for 2D Chern…
We present a first-principles scheme that allows the orbital magnetization of a magnetic crystal to be evaluated accurately and efficiently even in the presence of complex Fermi surfaces. Starting from an initial electronic-structure…
We introduce a model to describe the wide shear zones observed in modified Couette cell experiments with granular material. The model is a generalization of the recently proposed approach based on a variational principle. The instantaneous…
We consider an arbitrary square integrable function $F$ on the phase space and look for the Wigner function closest to it with respect to the $L^2$ norm. It is well known that the minimizing solution is the Wigner function of any…
Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is known to host the FQHE, but not all Chern bands are suitable…
We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity…
In this note we demonstrate that locally optimal functional quantizers for probability distributions on a Banach space lying in the support of $P$ behave exactly like globally optimal functional quantizers in terms of…
Motivated by the analysis of gapped periodic quantum systems in presence of a uniform magnetic field in dimension $d \le 3$, we study the possibility to construct spanning sets of exponentially localized (generalized) Wannier functions for…
Our work aims at simulating and predicting the temperature conditions inside a power transformer using Physics-Informed Neural Networks (PINNs). The predictions obtained are then used to determine the optimal placement for temperature…
The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by…
Commonly, a two-dimensional topological insulator is characterized by non-zero Chern numbers associated with its band structure. In our work, we present the experimental demonstration of an anomalous topological insulator, for which the…
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for…
We define Wannier functions for interacting systems, and show that the results on the localization of the Wannier functions for non-interacting systems carry over to the Wannier functions for interacting systems. In addition we demonstrate…
We study properties of an attractive-repulsive energy functional based on power-kernels, which can be used for halftoning of images. In the first part of this work, using a variational framework for probability measures, we examine…
We formulate Wannier orbital overlap population and Wannier orbital Hamilton population to describe the contribution of different orbitals to electron distribution and their interactions. These methods, which are analogous to the well known…
We propose a microscopic, weak-coupling mechanism by which generic Chern bands relax toward ideal bands. We consider coupling interacting electrons to a Caldeira-Leggett like Ohmic bosonic bath. Using the Born-Markov approximation, Slater…
We construct the least superharmonic majorant of a continuous function $g$ on the $d$-dimensional unit ball ($d \geq 2$) via a canonical sequential scheme. While classical theory identifies this majorant with the value function of the…
Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…
Robust fractional charge localized at disclination defects has been recently found as a topological response in $C_{6}$ symmetric 2D topological crystalline insulators (TCIs). In this article, we thoroughly investigate the fractional charge…
This survey synthesizes the current state of the art on the regularity theory for solutions to the optimal partition problem. Namely, we consider non-negative, vector-valued Sobolev functions whose components have mutually disjoint support,…