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第684行：
第684行： − 在液体和稠密气体中，在一次碰撞后立即抛弃粒子之间的关联是无效的。Bbgky 层次结构(Bogoliubov-Born-Green-Kirkwood-Yvon 层次结构)提供了一种推导 boltzmann 型方程的方法，但也将它们扩展到稀释气体情况之外，包括在几次碰撞之后的相关性。+ 第692行：
第692行： − + 第698行：
第698行： − 在 Keldysh 公式中发现了包含随机动力学的量子方法。这种方法常用于电子量子输运计算。+ 第704行：
第704行： − +
→Stochastic methods
In liquids and dense gases, it is not valid to immediately discard the correlations between particles after one collision. The BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) gives a method for deriving Boltzmann-type equations but also extending them beyond the dilute gas case, to include correlations after a few collisions.
In liquids and dense gases, it is not valid to immediately discard the correlations between particles after one collision. The BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) gives a method for deriving Boltzmann-type equations but also extending them beyond the dilute gas case, to include correlations after a few collisions.
在液体和稠密气体中，不能在一次碰撞后立即丢掉粒子之间的关联。BBGKY 层级结构(Bogoliubov-Born-Green-Kirkwood-Yvon 层级结构)提供了一种推导玻尔兹曼型方程的方法，但也可以将它们扩展到稀薄气体情况之外，包括在几次碰撞之后的相关性。
|3 = Keldysh formalism (a.k.a. NEGF—non-equilibrium Green functions):
|3 = Keldysh formalism (a.k.a. NEGF—non-equilibrium Green functions):
| 3 Keldysh 形式主义。NEGF—non-equilibrium Green functions):
| 3 Keldysh 公式。NEGF—非平衡态格林函数):
A quantum approach to including stochastic dynamics is found in the Keldysh formalism. This approach often used in electronic [[quantum transport]] calculations.
A quantum approach to including stochastic dynamics is found in the Keldysh formalism. This approach often used in electronic [[quantum transport]] calculations.
A quantum approach to including stochastic dynamics is found in the Keldysh formalism. This approach often used in electronic quantum transport calculations.
A quantum approach to including stochastic dynamics is found in the Keldysh formalism. This approach often used in electronic quantum transport calculations.
人们在 Keldysh 公式中发明了包含随机动力学的量子方法，这种方法常用于电子量子输运计算。
|4 = Stochastic [[Liouville's theorem (Hamiltonian)|Liouville equation]]
|4 = Stochastic [[Liouville's theorem (Hamiltonian)|Liouville equation]]
|4 = Stochastic Liouville equation
|4 = Stochastic Liouville equation
| 4随机 Liouville 方程
| 4随机 刘维尔方程
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