高知工科大学 統合量子素子研究室セミナー
オンジェイ・トゥレク博士（チェコ・オストラヴァ大学講師）平成30年10月31日
Kochi University of Technology
Unified Quantum Device Laboratory Seminar
⭐Speaker: Dr. Ondrej Turek (Assistant Professor, University of Ostrava, Czechia)
⭐Date&Time : 10 /31 /2018 (Wed) 14:40-16:10
⭐Place: Kami Campus, B555
⭐Title: Bethe-Sommerfeld conjecture in quantum mechanics on graphs
⭐Abstract:
A conjecture formulated by Bethe and Sommerfeld in 1933 states that any quantum system that is periodic in more than one direction has a finite number of gaps in its spectrum. The conjecture was proved for numerous systems, but it turned out to be invalid for periodic quantum graphs, the spectra of which usually have either infinitely many gaps, or no gaps at all. In the talk, we will present the very first example a periodic quantum graph that has a nonzero finite number of gaps in its spectrum, and we will discuss the problem of constructing periodic quantum graphs featuring a given exact number of spectral gaps.
References
[1] Pavel Exner, Ondřej Turek, Nanosystems: Phys. Chem. Math. 8 (2017), 305-309
[2] Pavel Exner, Ondřej Turek, J. Phys. A: Math. Theor. 50 (2017) 455201
[3] Ondřej Turek, arXiv.org:1801.02572
[4] Jaroslav Hančl, Ondřej Turek, arXiv.org:1809.01013
♦️presentation material [PDF] download
[ turek2018kut ]
