ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
We examine the distribution of normal-mode coordinates (defined via the eigenvectors of a chain of harmonic oscillators) for a system of purely repulsive hard rods in one dimension. We obtain an exact solution for the singlet density distribution, and separately for the covariances of the normal-mode coordinates. The hard-rod behavior is examined in terms of its deviation from the corresponding distributions for the system of harmonic oscillators. All off-diagonal covariances are zero in the hard-rod system, and the (on-diagonal) variances vary with the normal-mode wave number exactly as in the harmonic system. The detailed singlet normal-mode density distributions are very smooth but nonanalytic, and they differ from the (Gaussian) distributions of the corresponding harmonic system. However, all of the normal-mode coordinate distributions differ in roughly the same way when properly scaled by the distribution variance, and the differences vanish as 1/N in the thermodynamic limit of an infinite number of particles N. © 1999 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.479080
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