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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Random Matrices & Universality<br />
Universality classes<br />
Depending on the symmetry properties of the system one uses ensembles<br />
form<br />
orthogonal (β = 1);<br />
unitary (β = 2) and<br />
symplectic (β = 4) ensembles.<br />
The exponent β determines the level repulsion, P(s) ∼ s β for s → 0 where<br />
s stands for the (normalised) level spacing, si = φi+1 − φi.<br />
see e.g. F. Haake, Quantum Signatures of Chaos<br />
K ˙Z (IF UJ/CFT PAN ) <strong>Level</strong> <strong>Spacing</strong> <strong>Distribution</strong> March 14, 2011 3 / 20
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