Level Spacing Distribution Revisited - Theoretical Group Atomic ...
Level Spacing Distribution Revisited - Theoretical Group Atomic ...
Level Spacing Distribution Revisited - Theoretical Group Atomic ...
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Average minimal spacing 〈smin〉 for large unitary<br />
matrices<br />
Approximation of independent spacings<br />
Assume spacings sj described by the distribution Pβ(s) are independent.<br />
Minimal spacing<br />
Since for small spacings Pβ(s) ∼ s β so the integrated distribution<br />
I(s) = s<br />
0 P(s′ )ds ′ behaves as Iβ(s) ∼ s 1+β<br />
Matrix of order N yields N spacings sj. The minimal spacing smin occurs<br />
for such an argument that Iβ(smin) ≈ 1/N.<br />
Thus (smin) 1+β ≈ 1/N =⇒ smin ≈ N −β−1<br />
K ˙Z (IF UJ/CFT PAN ) <strong>Level</strong> <strong>Spacing</strong> <strong>Distribution</strong> March 14, 2011 18 / 20
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