Bound states of the Schrödinger-Newton model in low dimensions

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Light and sound waves can move objects through the transfer of linear or angular momentum, which has led to the development of optical and acoustic tweezers, with applications ranging from biomedical engineering to quantum optics. Although impressive manip ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wea ...

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few s ...

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

It has been observed that achiral nanoparticles, such as flat helices, may be subjected to an optical torque even when illuminated by normally incident linearly polarized light. However, the origin of this fascinating phenomenon has so far remained mostly ...

Bound states of the Schrödinger-Newton model in low dimensions

Chat with Graph Search

Wave-momentum shaping for moving objects in heterogeneous and dynamic media

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

From low-rank retractions to dynamical low-rank approximation and back

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Anomalous dissipation and other non-smooth phenomena in fluids

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Low-Rank Tensor Methods for High-Dimensional Problems

Single-shot Kramers-Kronig complex orbital angular momentum spectrum retrieval

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Multipolar Pseudochirality-Induced Optical Torque