用马尔可夫链方法导出硬棒混合物的精确密度泛函
Exact density functional for hard rod mixtures derived from Markov chain approach
摘要：
使用马尔可夫链的方法，我们重新推导出精确的密度泛函硬棒混合物的一维晶格，这构成了晶格基本测度理论的基础。马尔可夫链中的转移概率取决于一组占据数，这反映了零维腔最多容纳一个粒子的性质。对于给定的平均占有数（密度分布），得到了微观态平衡分布的精确表达式，这意味着产生平衡密度分布的唯一外势的表达式。考虑到杆端落在晶格位置上，混合物总是可加的。
英文摘要：
Using a Markov chain approach we rederive the exact density functional for hard rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain depends on a set of occupation numbers, which reflects the property of a zero-dimensional cavity to hold at most one particle. For given mean occupation numbers (density profile), an exact expression for the equilibrium distribution of microstates is obtained, that means an expression for the unique external potential that generates the density profile in equilibrium. By considering the rod ends to fall onto lattice sites, the mixture is always additive.
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