Second-Order Homogenization of Periodic Schrödinger Operators with Highly Oscillating Potentials
DOI10.1137/22m1478446arXiv2112.12008OpenAlexW4225484924MaRDI QIDQ6106295
Eric Cancès, David Gontier, Louis Garrigue
Publication date: 27 June 2023
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.12008
perturbation theorySchrödinger operatorsintegrated density of statesperiodic homogenizationdegenerate eigenvalues
Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Estimates of eigenvalues and eigenfunctions in periodic homogenization
- Semiclassical wave packet dynamics in Schrödinger equations with periodic potentials
- Homogenization of elliptic eigenvalue problems. I
- Homogenization of nonlinear reaction-diffusion equation with a large reaction term
- Some estimates from homogenization theory
- Semi-classical asymptotics in solid state physics
- A mathematical approach to the effective Hamiltonian in perturbed periodic problems
- Effective dynamics for Bloch electrons: Peierls substitution and beyond
- Spectral asymptotics for the Schrödinger operator on the line with spreading and oscillating potentials
- Homogenization of periodic systems with large potentials
- Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing
- Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials
- Third-order corrections in periodic homogenization for elliptic problem
- Numerical quadrature in the Brillouin zone for periodic Schrödinger operators
- Homogenization of the Schrödinger equation and effective mass theorems
- Operator estimates in homogenization theory
- Scattering, Homogenization, and Interface Effects for Oscillatory Potentials with Strong Singularities
- DISPERSIVE EFFECTIVE MODELS FOR WAVES IN HETEROGENEOUS MEDIA
- Développements asymptotiques des perturbations lentes de l'opérateur de schrödinger Périodique
- Defect Modes and Homogenization of Periodic Schrödinger Operators
- Semiclassical approximation for equations with periodic coefficients
- A Dispersive Effective Medium for Wave Propagation in Periodic Composites
- Homogenization and Two-Scale Convergence
- A General Convergence Result for a Functional Related to the Theory of Homogenization
- First-Order Corrections to the Homogenized Eigenvalues of a Periodic Composite Medium
- A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential
- Homogenization limits and Wigner transforms
- Semi-classical limits in a crystal with exterior potentials and effective mass theorems.
- First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
- Semiclassical asymptotics in magnetic Bloch bands
- Stochastic Homogenization of Linear Elliptic Equations: Higher-Order Error Estimates in Weak Norms Via Second-Order Correctors
- Second order periodic differential operators. Threshold properties and homogenization
- First-order expansions for eigenvalues and eigenfunctions in periodic homogenization
- Crime pays; homogenized wave equations for long times
- HOMOGENIZATION OF THE DIRICHLET PROBLEM FOR ELLIPTIC SYSTEMS: ‐OPERATOR ERROR ESTIMATES
- Localization for the Schrödinger Equation in a Locally Periodic Medium
This page was built for publication: Second-Order Homogenization of Periodic Schrödinger Operators with Highly Oscillating Potentials
