论文标题
气体中快速粒子的量子主方程
Quantum master equations for a fast particle in a gas
论文作者
论文摘要
在量子力学的背景下，研究了在热平衡下低密度气体中快速粒子的传播。管理粒子降低密度矩阵的红场形式中的量子主方程是从第一原理中明确得出的。在某些近似值下，该方程将减小为线性玻尔兹曼方程。还通过lindblad形式讨论了时间演变的积极性问题。详细讨论了这些方程式的出生和马尔可夫假设以及有关浴室相关函数的其他近似值。此外，如果粒子的密度基质在动量的基础上是对角线，或者碰撞速率与粒子动量无关，则所有这些主方程彼此相等。
The propagation of a fast particle in a low-density gas at thermal equilibrium is studied in the context of quantum mechanics. A quantum master equation in the Redfield form governing the reduced density matrix of the particle is derived explicitly from first principles. Under some approximations, this equation reduces to the linear Boltzmann equation. The issue of the positivity of the time evolution is also discussed by means of a Lindblad form. The Born and Markov assumptions underlying these equations, as well as other approximations regarding the bath correlation function, are discussed in details. Furthermore, all these master equations are shown to be equivalent with each other if the density matrix of the particle is diagonal in the momentum basis, or if the collision rate is independent of the particle momentum.
