Linear-Network Model for Magnetic Breakdown in Two Dimensions

On the measure of the spectrum for the almost Mathieu operator

“…There are q regions where it passes monotonically from 2 to -2 [15]. Schematics are shown in Fig As with so much else in the study of the almost Mathieu equation, our analysis depends on a remarkable formula of Chambers [6] and Butler-Brown [5] giving…”

Chambers’s Formula for the Graphene and the Hou Model with Kagome Periodicity and Applications

“…The aim of this article is to prove that, for a model considered by Hou [16], there exists a formula which is similar to the one obtained by Chambers [8] for the Harper model and describe the dependence of the characteristic polynomial on the quasi-momenta (θ 1 , θ 2 ). (see also Helffer-Sjöstrand [12,13], Bellissard-Simon [7], Kreft [20], Avron (and coauthors) [3]).…”

Stage III Annealing Study of Electron-Irradiated Pure Aluminum

“…Pippard 2 ' 3 has discussed the consequences of breakdown in terms of network models and the author has attempted to justify this approach in terms of a nearly-free-electron model 4 and in terms of the theory of the effective Hamiltonian. 5 A modified theory of the de Haas-van Alphen effect was developed by Falicov and Stachowiac 6 in terms of a time-dependent Green's function and a similar theory was later developed by the author in terms of a time-independent Green's function.…”

“…5 A modified theory of the de Haas-van Alphen effect was developed by Falicov and Stachowiac 6 in terms of a time-dependent Green's function and a similar theory was later developed by the author in terms of a time-independent Green's function. 4,5 Both approaches treat the Green's function as a propagator on a Pippard network.…”

“…[1][2][3][4][5][6][7][8][9] Federighi et al}~A in a series of experiments irradiated pure Al and Al alloys with neutrons. Recovery spectra in the Stage II and Stage III regions were investigated.…”