偏微分方程式セミナー(2016/7/1): 周期的に破損したカーボンナノチューブ上のシュレディンガー作用素のスペクトルについて, 新國 裕昭 氏 (前橋工科大学)

開催日時
2016年   7月 1日 16時 30分 ~ 2016年   7月 1日 18時 00分
場所
北海道大学理学部3号館3-309室
講演者
新國 裕昭 氏 (前橋工科大学)
 
Nowadays, we have a lot of opportunities to see that carbon nanotubes play roles as matrials in the fields of mechanical engineering due to their outstanding properties. In this talk, we study the spectra of carbon nanotubes from the point of view of quantum graphs. Namely, we examine the spectral properties of periodic Schr\"odinger operators on the metric graphs corresponding to carbon nanotubes. Especially, we deal with one of the simplest models of periodically broken carbon nanotubes. Utilizing the Floquet-Bloch theory, we show that its spectrum has the band-gap structure. Namely, we notice that its spectrum consists of the absolutely continuous spectrum and the set of eigenvalues with infinite multiplicities. Furthermore, we prove that the absolutely continuous spectrum is characterized by the corresponding discriminants and consists of infinitely many closed intervals. We note that our spectral discriminants are not entire functions but meromorphic functions, whereas the spectral discriminants for the standard Hill operators are entire.

関連項目

研究集会・セミナー・集中講義の一覧へ