A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations
DOI10.1016/j.jcp.2009.01.028zbMath1168.65056OpenAlexW2117969428MaRDI QIDQ1017593
Publication date: 12 May 2009
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2009.01.028
homogenizationSchrödinger equationBloch waveslevel set methodsemiclassical limithigh-frequency asymptoticsBloch eigenvalues
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
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Cites Work
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- Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. I: Homogeneous problems
- A level set based Eulerian method for paraxial multivalued traveltimes
- Superposition of multi-valued solutions in high frequency wave dynamics
- Geometric optics in a phase-space-based level set and Eulerian framework
- Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. II: Impurities, confinement and Bloch oscillations
- A level set framework for capturing multi-valued solutions of nonlinear first-order equations
- Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Theory of Bloch waves
- Radiative transport in a periodic structure
- On Wigner measures
- Effective dynamics for Bloch electrons: Peierls substitution and beyond
- High-frequency wave propagation by the segment projection method
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
- A PDE-based fast local level set method
- Local level set method in high dimension and codimension
- Gaussian beam construction for adiabatic perturbations
- A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations
- A level set-based Eulerian approach for anisotropic wave propagation
- An accurate spectral/discontinuous finite-element formulation of a phase-space-based level set approach to geometrical optics
- Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems
- Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. III: From ab initio models to WKB for Schrödinger-Poisson
- A level set method for three-dimensional paraxial geometrical optics with multiple point sources
- A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations
- Computational high-frequency wave propagation using the level set method with applications to the semi-classical limit of Schrödinger equations
- Strong Stability-Preserving High-Order Time Discretization Methods
- Two Approximations of Solutions of Hamilton-Jacobi Equations
- Transmission traveltime tomography based on paraxial Liouville equations and level set formulations
- Viscosity Solutions of Hamilton-Jacobi Equations
- A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential
- Homogenization limits and Wigner transforms
- Motion in periodic potentials
- Computational high frequency wave propagation
- A Bloch Decomposition–Based Split‐Step Pseudospectral Method for Quantum Dynamics with Periodic Potentials
- A Local Level Set Method for Paraxial Geometrical Optics
- The Effect of a Magnetic Field on Electrons in a Periodic Potential
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