DYNAMICS OF QUANTUM LEVEL-CROSSING SYSTEMS IN CONDENSED MATTER

研究了凝聚态平交道口耗散对非绝热过程的影响。本文利用考虑多模声子系统相互作用的扩展齐纳模型，通过对非对角矩阵元素的形式扰动序列的解析考虑，研究了水平交叉处的跃迁概率P。在各种物理参数的极限情况下，得到了P的封闭表达式。特别地，得到了非相干极限跃迁概率的一般公式，该公式既适用于高温极限，也适用于低温强耦合极限。此外，通过引入声子相互作用模式的阻尼超算子，对跃迁动力学进行了数值模拟。数值计算较好地再现了分析结果。此外，数值模拟还阐明了整个参数区域的动力学特性。该模型也适用于固体中局部中心的非辐射跃迁问题，如半导体中的DX中心。结果表明，系统被激发到绝热势曲线的上部区域，经过绝热势曲线的交叉区域，在松弛到激发态的热平衡之前，会发生向另一状态的热跃迁。

We have investigated the effect of dissipation on the nonadiabatic processes at a level-crossing in condensed matter. By a model of extended Zener model where the interaction with a system of many-mode phonons are taken into account, we have studied the transition probability P at a level crossing by analytical consideration for the formal perturbation series with respect to the off-diagonal matrix element. Colsed expressions for P are obtained in various limiting situations of the physical parameters. Especially, a general formula describing the transition probability in the incoherent limit was obtained, which covers both the high temperature limit and the low temperature strong coupling lmit. Furthermore, numerical simulations of the transition dynamics were performed by introducing the damping hyper operator for the interaction mode of the phonon. The analytical results are well reproduced by the numerical calculation. In addition, the dynamics all over the parameter region was clarified by the numerical simulation.The model was applied also to the problem of nonradiative transitions at localized centers in solids such as the DX centers in semiconductors. It is made clear that the system excited to the upper region of the adiabatic potential curves makes a hot transition to another state before it relaxs to the thermal equilibrium in the excited state, through the croosing region of the adiabatic potential curves.