藤本 茂雄

type:text [要旨] 弦の振動は波動現象としてよく知られたテーマであるが、共振状態と比べて非共振状態が扱われることは少なく、非共振状態の弦の様子を目にする機会は多くない。本研究では、シミュレーションを通じて非共振状態を体験する機会を得るために、両端を固定した弦の１点に周期的な外力を与えた際に生じる振動を取り上げ、その振動に現れる非共振状態と共振状態を観察可能なシミュレーションプログラムを開発した。シミュレーションでは利用者自身で外力の振動数を設定でき、非共振状態から共振状態への移り変わりの様子を観察可能である。加えて外力を与える位置も設定可能であり、位置の変化によって非共振状態から共振状態への移り変わりの様子が変化することを確認した。またLMSを通じた利用も考慮して、作成したシミュレーションプログラムをLMSとして広く利用されているMoodleで実行する方法についても説明する。

We study the electronic states of graphene nanoribbons whose edge structures are modified in the manner that Klein's bearded bonds are periodically distributed. In the triply periodic system, complete flat bands are obtained in the case that two Klein's bonds are attached to edge per unit cell. However, there is no flat band in one Klein's bond case. We discuss the existence of flat bands in the triple periodicity system in relation to the linkage between wavefunctions; the analytic expression of the wavefunction is consecutively derived by the transfer matrix method.

To investigate Fano resonances in the system of quantum dots (QDs), the conduction spectra for a fullerene C₆₀ is calculated in consideration of distortion effects for some characteristic modes. In mesoscopic systems, the Fano effect has mainly been observed in an Aharonov–Bohm (AB) ring system with a QD. In the present paper, we would like to stress that a referential path of an AB ring is not required to obtain asymmetric Fano resonances in C₆₀. The interference between a narrow peak and a long tail of a wide peak causes the Fano resonance in this molecule. The former plays the role of the discrete level and the latter the continuum state. These levels originate from a degenerate state through the effect of distortion. In particular, a dip structure giving zero conductance as the destructive interference appears in the cases of distortions with odd parity. In addition, another type of conductance dip is found at a multiply degenerate level when the electrodes are attached to C₆₀ without axial symmetry. This type of conductance dip, which is induced from the 4th-order self-energy term, is reported for the first time in this paper. The dependence of this dip on temperature is also discussed.