Avoided crossings in three coupled oscillators as a model system of acoustic bubbles

複数気泡モデルとしての三結合振動子に現れるavoided crossing

井田 真人

Ida, Masato

音響的に相互作用する三気泡の共振周波数と脈動位相について議論し、複数気泡系にavoided crossingが現れうることを示す。シンプルな結合振動子モデルを用い、気泡が三つ以上存在する場合には、その系の共振周波数がavoided crossingを起こしうることを明らかにする。さらに、気泡の脈動位相と遷移周波数[Ida, Phys. Lett. A 297, 210 (2002); Ida, J. Phys. Soc. Jpn. 71, 1214 (2002)]に注目することで、avoided crossing領域中のある点(そこでは三気泡系の共振周波数と遷移周波数が交わる)において、気泡間で明確な状態交換が行われることを示す。

The resonance frequencies and oscillation phases of three acoustically coupled bubbles are examined to show that avoided crossings can appear in a multibubble system. Via a simple coupled oscillator model, we show that if at least three bubbles exist, it is possible for their resonance frequencies to experience an avoided crossing. Furthermore, by focusing our attention on the oscillation phases and based on analysis of the transition frequencies [Ida, Phys. Lett. A 297, 210 (2002); Ida, J. Phys. Soc. Jpn. 71, 1214 (2002)] of the coupled bubbles, we show that a distinct state exchange takes place between the bubbles at a point in the avoided crossing region, where a resonance frequency of the triple-bubble system crosses with a transition frequency.