Frustrated quantum-spin system on a triangle coupled with ege_g lattice vibrations - Correspondence to Longuet-Higgins et al.'s Jahn-Teller model -

We investigate the quantum three spin model $({\bf S_1},{\bf S_2},{\bf S_3})$ of spin$=1/2$ on a triangle, in which spins are coupled with lattice-vibrational modes through the exchange interaction depending on distances between spin sites. The present model corresponds to the dynamic Jahn-Teller system $E_g\otimes e_g$ proposed by Longuet-Higgins {\it et al.}, Proc.R.Soc.A.{\bf 244},1(1958). This correspondence is revealed by using the transformation to Nakamura-Bishop's bases proposed in Phys.Rev.Lett.{\bf 54},861(1985). Furthermore, we elucidate the relationship between the behavior of a chiral order parameter ${\hat \chi}={\bf S_1\cdot(S_2\times S_3)}$ and that of the electronic orbital angular momentum ${\hat \ell_z}$ in $E_g\otimes e_g$ vibronic model: The regular oscillatory behavior of the expectation value $$for vibronic structures with increasing energy can also be found in that of$$. The increase of the additional anharmonicity(chaoticity) is found to yield a rapidly decaying irregular oscillation of $$

Chaos and its quantization in dynamical Jahn-Teller systems

We investigate the $E_g \otimes e_g$ Jahn-Teller system for the purpose to reveal the nature of quantum chaos in crystals. This system simulates the interaction between the nuclear vibrational modes and the electronic motion in non-Kramers doublets for multiplets of transition-metal ions. Inclusion of the anharmonic potential due to the trigonal symmetry in crystals makes the system nonintegrable and chaotic. Besides the quantal analysis of the transition from Poisson to Wigner level statistics with increasing the strength of anharmonicity, we study the effect of chaos on the electronic orbital angular momentum and explore the magnetic $g$-factor as a function of the system's energy. The regular oscillation of this factor changes to a rapidly-decaying irregular oscillation by increasing the anharmonicity (chaoticity).Comment: 8 pages, 6 figure

Effects of Non-Adiabatic Transitions on Proton Dynamics(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

この論文は国立情報学研究所の電子図書館事業により電子化されました。水素分子では反結合励起状態に置かれた波束はすぐに広がってしまう。これは水素分子が二つの水素に解離することに対応している。しかしながら、準位間遷移のために、波束のほんの少しは結合基底状態に落ちていく。本研究ではプロトン三つと電子一つの系の振る舞いをみた。準位開遷移を考慮に入れて計算した。計算では両側のプロトンを固定し、中央のプロトンの感じる断熱ポテンシャルを求めた。そのボテンシャル準位開の遷移はエネルギー的に接近している中心点で起こっていることがわかった