Nearest-Neighbor Spacing Distribution for an Ensemble of Random Matrices with a Nonrandom Bias

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Abstract
The nearest‐neighbor spacing distribution for the biased Gaussian distribution exp [−γ Tr (H − H0)2] is calculated in the limits of large and small γ. The results for the small‐γ limit are found to approach those for an unbiased Gaussian distribution (i.e., H0 proportional to the unit matrix). To order γ2 the mth‐order spacing distribution is expressed in terms of the mth‐order spacing distribution for the unbiased Gaussian ensemble. The results for the large‐γ limit are found to depend strongly on H0. That is, the nearest‐neighbor spacing distribution reflects the structure of H0. Thus, a biased distribution offers a possible description for the experimental deviations from the Wigner surmise and apparent multiple‐peak structure exhibited by some nuclear‐spacing data.