Frequency
spacing probes vibrational coupling
M. Mumpower, E. Bettelheim, TW
Count number of frequency
spacings xi ¼ wi+1 - wi
Simplest distribution: omegas
are random
Vibrations are decoupled
Number of pairs
P(x)
x
e-x
Spacings of lowest jammed modes
Number
w
Fits expected formula for coupled modes
(Wigner-Dyson
random matrix)x
P(x)
Thus, the anomalous modes are
coupled.