ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
We investigate one-dimensional chaotic configurations of atoms, which are generated by the Baker transformation or, equivalently, by the Bernoulli shift. The problem of calculating the distribution of the jth nearest-neighbor distances of these configurations is shown to be equivalent to the task of finding the limit distribution of the sum of the strongly dependent random variables Xl:([0,1),μL)→[0,1), x→(2lx)mod 1 (l∈N0, μL is the Lebesgue measure). We prove the validity of a local limit theorem for this sequence of random variables and conclude, therefore, that the distribution density Gj of the jth nearest-neighbor distances is asymptotically (as j→∞) a Gaussian distribution, the width of which grows as (j)1/2. With the aid of this result, we prove that the pair distribution function G of our configurations, which is the sum of the Gj's, tends to unity in the limit of large distances.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.526519
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