The Random Schrödinger Equation: Homogenization in Time-Dependent Potentials

DOI10.1137/15M1024986zbMath1339.60079arXiv1506.02728OpenAlexW2964325728MaRDI QIDQ2806410

Leonid Ryzhik, Yu Gu

Publication date: 18 May 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.02728

zbMATH Keywords

homogenizationrandom potentialkinetic limitrandom Schrödinger equation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Schrödinger operator, Schrödinger equation (35J10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (4)

Classical limit for the varying-mass Schrödinger equation with random inhomogeneities ⋮ Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium ⋮ Homogenization for the cubic nonlinear Schrödinger equation on R2 ⋮ The 1D Schrödinger equation with a spacetime white noise: the average wave function

Cites Work

• Asymptotics of the solutions of the stochastic lattice wave equation
• Convergence to SPDE of the Schrödinger equation with large, random potential
• Asymptotics of the solutions of the random Schrödinger equation
• Kinetic limit for wave propagation in a random medium
• Self-averaging of Wigner transforms in random media
• Kinetic limits for waves in a random medium
• Homogenization with Large Spatial Random Potential
• Homogenization limits and Wigner transforms
• Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
• Radiative transport limit for the random Schrödinger equation
• SELF-AVERAGING IN TIME REVERSAL FOR THE PARABOLIC WAVE EQUATION
• HOMOGENIZATION OF THE SCHRÖDINGER EQUATION WITH LARGE, RANDOM POTENTIAL
• Derivation of the transport equation for electrons moving through random impurities

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