On the controversy over the stochastic density functional equations

Details On the controversy over the stochastic density functional equations On the controversy over the stochastic density functional equations

2000-03-21

arxiv.org/abs/cond-mat/0003339v1

J. Phys. A: Math. Gen. vol. 33, L155 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages in IOP format, to be published in J. Phys. A

Scientific paper

10.1088/0305-4470/33/15/101

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 $P(\{\rho\},t)$. Moreover, we verify the associated static solution of $P(\{\rho\},t)$ with the help of the conditional grand canonical partition function.

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