On the controversy over the stochastic density functional equations

H. Frusawa; R. Hayakawa

doi:10.1088/0305-4470/33/15/101

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arXiv · cond-mat/0003339

On the controversy over the stochastic density functional equations

H. Frusawa·R. Hayakawa

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Abstract

This letter aims at justifying the stochastic equations in terms of the number density variable, which are still controversial, via complementing Dean's approach [Dean D S 1996 {\itshape J. Phys. A} {\bf 29} L613]. Our course is twofold: First, we demonstrate that standard manipulations straightforwardly transform the stochastic equation of density {\itshape operator}, derived by Dean, to the Fokker-Planck equation for the (c-number) density distribution functional $P(\{ρ\},t)$. Moreover, we verify the associated static solution of $P(\{ρ\},t)$ with the help of the conditional grand canonical partition function.

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H. Frusawa, R. Hayakawa. 2000-03-21. On the controversy over the stochastic density functional equations. https://doi.org/10.1088/0305-4470%2F33%2F15%2F101

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