A Result Not Dependent on Rationality for Bloch Electrons in a Magnetic Field
physica status solidi (b)Published 1 August 1978
Gregory H. Wannier
Citations240
SJR quartileQ3
SJR score0.38
SNIP0.57
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
Abstract There are some facts known about the wave functions of a Bloch electron in a magnetic field. A great deal more is known for a special model. All results are restricted to rational fields and depend heavily on the denominator of the representative fraction. A result is described below which is independent of rationality. It is the statistical weight of identifiable regions in an energy versus field plot. In fact if one goes further and plots instead of the energy the integrated density of state versus field a set of computable polygons results for these regions.
Keywords
Physics and Astronomy
Physical review. B, Solid stateEnergy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
3,495 Citations1976Douglas R. Hofstadter
The European Physical Journal AZur Theorie des Diamagnetismus von Leitungselektronen
1,353 Citations1933R. Peierls
The London Edinburgh and Dublin Philosophical Magazine and Journal of ScienceInterpretation of the de Haas-van Alphen effect
692 Citations1952Lars Onsager
Physical ReviewDecoupling of Bloch Bands in the Presence of Homogeneous Fields
73 Citations1962Gregory H. Wannier, D. R. Fredkin
physica status solidi (b)Bloch Electrons in Irrational Magnetic Fields
69 Citations1974Alexander Rauh, Gregory H. Wannier +1 more
physica status solidi (b)Bloch Electrons in Magnetic Fields. Rationality, Irrationality, Degeneracy
18 Citations1976G. Obermair, Gregory H. Wannier
physica status solidi (b)Invariance Properties of a Proposed Hamiltonian for Bloch Electrons in a Magnetic Field
17 Citations1975Gregory H. Wannier