论文标题
将投影算子方法应用于具有瞬态电势的粗粒动力学
Application of Projection Operator Method to Coarse-Grained Dynamics with Transient Potential
论文作者
论文摘要
我们表明，具有时间依赖性和波动电势（瞬态电位）的粗粒动力学模型可以源自微观哈密顿动力学。瞬态电位的概念首先是在现象学上引入的，并且尚未阐明其与基本微观动力学的关系。这与广义的langevin方程相反，该方程与微观动力学的关系是完善的。在这项工作中，我们表明，具有瞬态电势的动态方程可以为耦合振荡器模型得出，而无需任何近似值。众所周知，耦合振荡器模型的动力学可以由广义Langevin类型方程进行精确描述。这一事实意味着，具有瞬态电势的动态方程可以用与广义langevin方程相似的方式用作粗粒粒度的动力学模型。然后，我们证明了瞬态电势的动力方程也可以正式地用于微观汉密尔顿动力学，而无需任何近似值。我们使用投影算子方法来进行粗粒变量和瞬态势。粗粒位置和动量的动态方程与哈密顿动力学中的动力学方程相似，但是相互作用电位被瞬态电势取代。瞬态电势的动态方程是具有内存效应的广义Langevin方程。我们的结果证明了瞬态电位描述粗粒动力学的合理性。我们提出了几个近似值来获得简化的动力学模型。我们表明，在几个近似值下，瞬态电势的动态方程将减少到相对简单的马尔可夫动态方程中，对于潜在参数。
We show that the coarse-grained dynamics model with the time-dependent and fluctuating potential (transient potential) can be derived from the microscopic Hamiltonian dynamics. The concept of the transient potential was first introduced rather phenomenologically, and its relation to the underlying microscopic dynamics has not been clarified yet. This is in contrast to the generalized Langevin equation, of which relation to the microscopic dynamics is well-established. In this work, we show that the dynamic equations with the transient potential can be derived for the coupled oscillator model, without any approximations. It is known that the dynamics of the coupled oscillator model can be exactly described by the generalized Langevin type equations. This fact implies that the dynamic equations with the transient potential can be utilized as a coarse-grained dynamics model in a similar way to the generalized Langevin equation. Then we show that the dynamic equations for the transient potential can be also formally derived for the microscopic Hamiltonian dynamics, without any approximations. We use the projection operator method for the coarse-grained variables and transient potential. The dynamic equations for the coarse-grained positions and momenta are similar to those in the Hamiltonian dynamics, but the interaction potential is replaced by the transient potential. The dynamic equation for the transient potential is the generalized Langevin equation with the memory effect. Our result justifies the use of the transient potential to describe the coarse-grained dynamics. We propose several approximations to obtain simplified dynamics model. We show that, under several approximations, the dynamic equation for the transient potential reduces to the relatively simple Markovian dynamic equation for the potential parameters.
