Publications related to Initial or final values for semiclassical evolutions in the Weyl–Wigner representation

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key fea ...

World Scientific Publ Co Pte Ltd2024

An interior penalty coupling strategy for isogeometric non-conformal Kirchhoff-Love shell patches

Annalisa Buffa, Pablo Antolin Sanchez, Giuliano Guarino

This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the C 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag ...

Springer2024

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

Joachim Stubbe, Luigi Provenzano, Paolo Luzzini, Davide Buoso

We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper ...

SPRINGER2023

DeepBND: A machine learning approach to enhance multiscale solid mechanics

Annalisa Buffa, Simone Deparis, Pablo Antolin Sanchez, Felipe Figueredo Rocha

Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local PDE and some aver ...

2023

Wigner Formulation of Thermal Transport in Solids

Nicola Marzari, Michele Simoncelli

Two different heat-transport mechanisms are discussed in solids. In crystals, heat carriers propagate and scatter particlelike as described by Peierls's formulation of the Boltzmann transport equation for phonon wave packets. In glasses, instead, carriers ...

AMER PHYSICAL SOC2022

Perimeter Modes of Nanomechanical Resonators Exhibit Quality Factors Exceeding 10(9) at Room Temperature

Tobias Kippenberg, Guanhao Huang, Alberto Beccari, Amirali Arabmoheghi, Nils Johan Engelsen, Sergey Fedorov

Systems with low mechanical dissipation are extensively used in precision measurements such as gravitational wave detection, atomic force microscopy, and quantum control of mechanical oscillators via optomechanics and electromechanics. The mechanical quali ...

AMER PHYSICAL SOC2022

Wigner Measures and Coherent Quantum Control

Tudor Ratiu

We introduce Wigner measures for infinite-dimensional open quantum systems; important examples of such systems are encountered in quantum control theory. In addition, we propose an axiomatic definition of coherent quantum feedback. ...

2021

Decay for the nonlinear KdV equations at critical lengths

Hoài-Minh Nguyên

We consider the nonlinear Korteweg-de Vries (KdV) equation in a bounded interval equipped with the Dirichlet boundary condition and the Neumann boundary condition on the right. It is known that there is a set of critical lengths for which the solutions of ...

2020

Weyl-type bounds for Steklov eigenvalues

Joachim Stubbe, Luigi Provenzano

We present upper and lower bounds for Steklov eigenvalues for domains in RN+1 with C-2 boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds on Riesz-means and the trace of corresponding Steklov heat kernel. The key res ...

EUROPEAN MATHEMATICAL SOC2019

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Marius Christopher Lemm, Rui Han

We study the one-dimensional discrete Schrödinger operator with the skew-shift potential

2\lambda\cos\left(2\pi \left(\binom{j}{2} \omega+jy+x\right)\right)

. This potential is long conjectured to behave like a random one, i.e., it is expected to produce ...

2018

Initial or final values for semiclassical evolutions in the Weyl–Wigner representation

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Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

An interior penalty coupling strategy for isogeometric non-conformal Kirchhoff-Love shell patches

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

DeepBND: A machine learning approach to enhance multiscale solid mechanics

Wigner Formulation of Thermal Transport in Solids

Perimeter Modes of Nanomechanical Resonators Exhibit Quality Factors Exceeding 10(9) at Room Temperature

Wigner Measures and Coherent Quantum Control

Decay for the nonlinear KdV equations at critical lengths

Weyl-type bounds for Steklov eigenvalues

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

An interior penalty coupling strategy for isogeometric non-conformal Kirchhoff-Love shell patches

Decay for the nonlinear KdV equations at critical lengths

Perimeter Modes of Nanomechanical Resonators Exhibit Quality Factors Exceeding 10(9) at Room Temperature

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

Wigner Formulation of Thermal Transport in Solids

Wigner Measures and Coherent Quantum Control

Weyl-type bounds for Steklov eigenvalues

DeepBND: A machine learning approach to enhance multiscale solid mechanics

Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres