Concept
Théorie spectrale
Publications associées (107)
A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation
- Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...
Transition to chaos in extended systems and their quantum impurity models
Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model ...
Bristol2024Turbulence in the Strongly Heterogeneous Near-Surface Boundary Layer over Patchy Snow
Michael Lehning, Dylan Stewart Reynolds, Michael Haugeneder
The near-surface boundary layer above patchy snow cover in mountainous terrain is characterized by a highly complex interplay of various flows on multiple scales. In this study, we present data from a comprehensive field campaign that cover a period of 21 ...
2024Deep Learning Meets Sparse Regularization
Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...
2023Spectral analysis for transmission eigenvalue problems with and without the complementing conditions
The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...
EPFL2022Spectral Hypergraph Sparsifiers of Nearly Linear Size
Mikhail Kapralov, Jakab Tardos
Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which optimal bounds on ...
IEEE COMPUTER SOC2022Unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials
Nicola Marzari, Tommaso Chiarotti, Andrea Ferretti
Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we propose a novel t ...
AMER PHYSICAL SOC2022