Gabor frames of Gaussian beams for the Schrödinger equation

DOI10.1016/j.acha.2015.11.001zbMath1362.42061arXiv1501.04949OpenAlexW2962985075MaRDI QIDQ2397166

Fabio Nicola, Michele Berra, Elena Cordero, Iulia Martina Bulai

Publication date: 29 May 2017

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.04949

zbMATH Keywords

Schrödinger equationGabor framesGaussian beamsmetaplectic operators

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Fourier integral operators applied to PDEs (35S30) Pseudodifferential operators (47G30)

Related Items

Computing quantum dynamics in the semiclassical regime, Stability of Gabor frames under small time Hamiltonian evolutions, Semi-classical time-frequency analysis and applications, Symplectic coarse-grained classical and semclassical evolution of subsystems: New theoretical approach

Uses Software

• Linear Time Frequency Analysis Toolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Schrödinger equations with rough Hamiltonians
• Fast multiscale Gaussian beam methods for wave equations in bounded convex domains
• A parametrix construction for the wave equation with low regularity coefficients using a frame of Gaussians
• Born-Jordan quantization and the equivalence of the Schrödinger and Heisenberg pictures
• Coherent states and applications in mathematical physics.
• Approximation of Fourier integral operators by Gabor multipliers
• Exponentially sparse representations of Fourier integral operators
• Gabor frames with Hermite functions
• Time-frequency analysis of Fourier integral operators
• Banach algebras of pseudodifferential operators and their almost diagonalization
• Sparsity of Gabor representation of Schrödinger propagators
• Gaussian beam decomposition of high frequency wave fields
• Foundations of time-frequency analysis
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Phase space analysis of semilinear parabolic equations
• Deformation of Gabor systems
• Wave packet analysis of Schrödinger equations in analytic function spaces
• Hamiltonian deformations of Gabor frames: first steps
• Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
• Gabor representations of evolution operators
• Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation
• THE LINEAR TIME FREQUENCY ANALYSIS TOOLBOX
• Recovery of High Frequency Wave Fields from Phase Space–Based Measurements
• Symplectic Methods in Harmonic Analysis and in Mathematical Physics
• Harmonic analysis of the de Rham complex on the sphere.
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• Varying the time-frequency lattice of Gabor frames
• Deforming gabor frames by quadratic hamiltonians
• Time-Frequency Analysis of Schrödinger Propagators
• Error estimates for Gaussian beam superpositions
• A Convergent Multiscale Gaussian-Beam Parametrix for the Wave Equation
• Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials
• Dilation of the Weyl symbol and Balian-Low theorem
• A Class of Nonharmonic Fourier Series