Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-05-21
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
We discuss necessary conditions for the existence of probability distribution on particle configurations in $d$-dimensions i.e. a point process, compatible with a specified density $\rho$ and radial distribution function $g({\bf r})$. In $d=1$ we give necessary and sufficient criteria on $\rho g({\bf r})$ for the existence of such a point process of renewal (Markov) type. We prove that these conditions are satisfied for the case $g(r) = 0, r < D$ and $g(r) = 1, r > D$, if and only if $\rho D \leq e^{-1}$: the maximum density obtainable from diluting a Poisson process. We then describe briefly necessary and sufficient conditions, valid in every dimension, for $\rho g(r)$ to specify a determinantal point process for which all $n$-particle densities, $\rho_n({\bf r}_1, ..., {\bf r}_n)$, are given explicitly as determinants. We give several examples.
Costin Ovidiu
Lebowitz Joel. L.
No associations
LandOfFree
On the Construction of Particle Distributions with Specified Single and Pair Densities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Construction of Particle Distributions with Specified Single and Pair Densities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Construction of Particle Distributions with Specified Single and Pair Densities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-679462