Spectral correlations in the optical phonon spectrum of a solid with a comp
lex unit cell are analyzed using the Wigner-Dyson statistical approach. Des
pite the fact that all force constants are real, we find that the statistic
s are predominantly of the GUE type depending on the location within the Br
illouin zone of a crystal and the unit cell symmetry. Analytic and numerica
l results for the crossover from GOE to GUE statistics are presented.