Convergence in higher mean of a random Schrödinger to a linear Boltzmann evolution

DOI10.1007/s00220-006-0085-2zbMath1190.82021arXivmath-ph/0407037OpenAlexW2029081836MaRDI QIDQ882980

Thomas Chen

Publication date: 31 May 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0407037

zbMATH Keywords

Boltzmann equationSchrödinger equationWigner transforms

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random linear operators (47B80)

Related Items (8)

Asymptotics of resolvent integrals: The suppression of crossings for analytic lattice dispersion relations ⋮ High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat ⋮ The weak coupling limit for the random Schrödinger equation: the average wave function ⋮ Notes on coherent backscattering from a random potential ⋮ Boltzmann limit and quasifreeness for a homogeneous Fermi gas in a weakly disordered random medium ⋮ Boltzmann limit for a homogeneous Fermi gas with dynamical Hartree-Fock interactions in a random medium ⋮ Single scattering estimates for the scintillation function of waves in random media ⋮ Dynamical typicality: Convergence of time evolved macro-observables to their mean values in random matrix models

Cites Work

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• Kinetic limit for wave propagation in a random medium
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Localization at large disorder and at extreme energies: an elementary derivation
• Frequency concentration and location lengths for the Anderson model at small disorders
• Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field
• Quantum diffusion of the random Schrödinger evolution in the scaling limit. II: The recollision diagrams
• Localization lengths and Boltzmann limit for the Anderson model at small disorders in dimension 3
• Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
• Derivation of the transport equation for electrons moving through random impurities

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