Quantum-classical dynamics of wave fields.
Quantum-classical dynamics of wave fields.
复制标题
波场的量子经典动力学。
作者：
A. Sergi
最近提出的相空间相关算符的量子经典力学方法被改造为波场的形式。这样的波场服从一个耦合的非线性方程组，该方程组可以用适当的非哈密顿括号写成。作为例子，该理论被应用于自旋-玻色子模型的驰豫动力学。在绝热极限下，计算结果与算符方法的计算结果吻合较好。此外，本文提出的理论可以考虑非绝热效应，而不需要采用表面跳跃近似。因此，所得到的结果与以前的表面跳跃计算结果定性地一致，并且增加了(至少)2倍，这是非绝热动力学可以以很小的统计误差传播的时间长度。此外，值得注意的是，这里提出的量子经典波场动力学是Weinberg最近提出的非线性量子力学形式的直接非哈密顿推广。
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surface-hopping approximations. Hence, the results obtained follow qualitatively those of previous surface-hopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantum-classical wave fields proposed here is a straightforward non-Hamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.