用过程模拟量子力学过程纳米粒子内振荡在相空间中的能量分布
Modelling Quantum Mechanical Processes by Processes Energy Distribution of Inner Oscillations of a Nanoparticle in the Phase Space
摘要：
考虑了在一定温度下，当纳米粒子在热平衡介质中运动时，其相空间内的内谐振荡能量分布的计算问题。假设粒子在介质和势函数所给力场的作用下服从布朗运动。在本文中，我们提供和研究的方程描述的问题，推广的Klein-Kramers方程。结果表明，当介质电阻较大时，纳米粒子内谐振荡的能量分布过程表现为一个快跃迁过程和一个慢跃迁过程的组合。在快速过渡过程之后，系统进入准稳态。慢过程近似地由用于描述量子过程的标准薛定谔方程描述。因此，所研究的过程可以作为量子过程的模型。
英文摘要：
We consider the problem of computing energy distribution of inner harmonic oscillations of a nanoparticle in its phase space, when the particle moves in a medium in heat equilibrium under certain temperature. It is assumed that the particle obeys the Brownian motion under the action of the medium and the force field given by a potential function. In the present paper we provide and study an equation describing the problem, generalizing the Klein--Kramers equation. It is shown that for large value of medium resistance, the process of energy distribution of inner harmonic oscillations of the nanoparticle is represented as the composition of a rapid transition process and a slow process. After the rapid transition process, the system goes to a quasi-stationary state. The slow process is approximately described by the standard Schrodinger equation used for description ofquantum processes. Thus, the process being studied can serve as a model of quantum processes.
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