Classical limit for the varying-mass Schrödinger equation with random inhomogeneities

DOI10.1016/j.jcp.2021.110365OpenAlexW3153899891MaRDI QIDQ2124409

Xu Yang, Shi Chen, Qin Li

Publication date: 11 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.05277

zbMATH Keywords

radiative transfersemiclassical limitrandom inhomogeneitiesvarying-mass Schrödinger equation

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) General mathematical topics and methods in quantum theory (81Qxx)

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Cites Work

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• A device adaptive inflow boundary condition for Wigner equations of quantum transport
• Semiclassical wave packet dynamics in Schrödinger equations with periodic potentials
• Accuracy of transport models for waves in random media
• Asymptotics of the solutions of the random Schrödinger equation
• Accurate calculation of Green's function of the Schrödinger equation in a block layered potential
• Kinetic limit for wave propagation in a random medium
• Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations
• Transport equations for elastic and other waves in random media
• Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
• On Wigner measures
• Classical and quantum transport in random media.
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Homogenization of periodic systems with large potentials
• Numerical approximations of singular source terms in differential equations
• Efficient implementation of weighted ENO schemes
• Semi-classical models for the Schrödinger equation with periodic potentials and band crossings
• Delta function approximations in level set methods by distance function extension
• Kinetic limits for waves in a random medium
• A semiclassical transport model for two-dimensional thin quantum barriers
• Homogenization of the Schrödinger equation and effective mass theorems
• The random Schrödinger equation: slowly decorrelating time-dependent potentials
• The Random Schrödinger Equation: Homogenization in Time-Dependent Potentials
• Convergence of frozen Gaussian approximation for high-frequency wave propagation
• Homogenization limits and Wigner transforms
• Semi-classical limits in a crystal with exterior potentials and effective mass theorems.
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
• Radiative transport limit for the random Schrödinger equation
• Laser Beam Imaging from the Speckle Pattern of the Off-Axis Scattered Intensity
• Wave Propagation and Imaging in Moving Random Media
• A Wigner-Measure Analysis of the Dufort--Frankel Scheme for the Schrödinger Equation
• Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport
• A Semiclassical Transport Model for Thin Quantum Barriers
• Effective Mass Theorems for Nonlinear Schrödinger Equations
• Derivation of the transport equation for electrons moving through random impurities
• An introduction to semiclassical and microlocal analysis