DYNAMICS OF QUANTUM LEVEL-CROSSING SYSTEMS IN CONDENSED MATTER

我们研究了耗散对凝聚态中能级交叉的非绝热过程的影响。通过考虑与多模声子系统相互作用的扩展Zener模型，通过解析考虑形式微扰级数相对于非对角矩阵元，研究了能级交叉处的跃迁几率P。在各种物理参数的极限情况下，得到了P的闭合表达式。特别地，得到了描述非相干极限跃迁几率的一般公式，该公式涵盖了高温极限和低温强耦合LMIT。此外，通过引入阻尼超算符对声子的相互作用模式进行了跃迁动力学的数值模拟。数值计算很好地再现了分析结果。该模型还适用于半导体中DX中心等固体中局域中心的非辐射跃迁问题。结果表明，被激发到绝热势能曲线上端的系统在松弛到激发态热平衡之前，会通过绝热势能曲线的低峰区发生热转变到另一个态。

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.