Some mathematical aspects of Anderson localization: boundary effect, multimodality, and bifurcation

DOI10.1088/1572-9494/ac7a1ezbMath1516.82044arXiv2112.13913OpenAlexW4225508092MaRDI QIDQ6157080

Ziqi Liu, Chen Jia, Zhimin Zhang

Publication date: 19 June 2023

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

Full work available at URL: https://arxiv.org/abs/2112.13913

zbMATH Keywords

eigenvalueeigenmodeSchrödinger operatorspectrumeigenfunctionelliptic operatorconfinementlandscape

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Quantum equilibrium statistical mechanics (general) (82B10)

Cites Work

• Mathematical theory of nonequilibrium steady states. On the frontier of probability and dynamical systems.
• Martingale structure for general thermodynamic functionals of diffusion processes under second-order averaging
• Geometrical Structure of Laplacian Eigenfunctions
• Localization of quantum states and landscape functions
• R-matrix theory with Dirichlet boundary conditions for integrable electron waveguides
• Diffusions and Elliptic Operators
• Computing Spectra without Solving Eigenvalue Problems
• Two-parameter localization for eigenfunctions of a Schrödinger operator in balls and spherical shells
• Localization and landscape functions on quantum graphs
• Localization of eigenfunctions via an effective potential

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