کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
838682 | 908366 | 2008 | 22 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Impurity bands and quasi-Bloch waves for a one-dimensional model of modulated crystal Impurity bands and quasi-Bloch waves for a one-dimensional model of modulated crystal](/preview/png/838682.png)
This paper investigates a simple one-dimensional model of incommensurate “harmonic crystal” in terms of the spectrum of the corresponding Schrödinger equation. Two angles of attack are studied: the first exploits techniques borrowed from the theory of quasi-periodic functions while the second relies on periodicity properties in a higher-dimensional space. It is shown that both approaches lead to essentially the same results; that is, the lower spectrum is split between “Cantor-like zones” and “impurity bands” to which correspond critical and extended eigenstates, respectively. These “new bands” seem to emerge inside the band gaps of the unperturbed problem when certain conditions are met and display a parabolic nature. Numerical tests are extensively performed on both steady and time-dependent problems.
Journal: Nonlinear Analysis: Real World Applications - Volume 9, Issue 3, July 2008, Pages 927–948