Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase

DOI10.1007/s10255-011-0095-5zbMath1278.81084OpenAlexW2046984064MaRDI QIDQ385173

Xu Yang, Jian-feng Lu, E. Weinan

Publication date: 2 December 2013

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-011-0095-5

zbMATH Keywords

asymptotic analysissemiclassical limitBerry phaseBloch dynamicsBloch-Wigner transform

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (6)

Bloch dynamics with second order Berry phase correction ⋮ Mathematical aspects of the Kubo formula for electrical conductivity with dissipation ⋮ Waves in Slowly Varying Band-Gap Media ⋮ Effective Maxwell equations from time-dependent density functional theory ⋮ Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature ⋮ Wave Packets in the Fractional Nonlinear Schrödinger Equation with a Honeycomb Potential

Cites Work

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• Semiclassical asymptotics in magnetic Bloch bands
• Semiclassical limit for the Schrödinger‐Poisson equation in a crystal
• Motion of Electrons in Adiabatically Perturbed Periodic Structures

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