Evolution of zero-dispersion peaks in fluctuation spectra with temperature

Zero-dispersion peaks (ZDPs) can arise in fluctuation spectra of underdamped systems for which the dependence of the eigenfrequency on energy has an extremum. It is shown that ZDPs exist only for temperatures T higher than the critical one, Tc. The shape of the ZDP is described analytically as well as the process of the onset of this peak at T ≈ Tc. In the low-friction limit the shape of the ZDP turns out to be universal for T > Tc.