Quasinormal Mode

Quasinormal Mode

Quasinormal modes (QNM) are the modes of energy dissipation of a perturbed object or field, i.e. they describe perturbations of a field that decay in time. A familiar example is the perturbation (gentle tap) of a wine glass with a knife: the glass begins to ring, it rings with a set, or superposition, of its natural frequencies -- its modes of sonic energy dissipation. One could call these modes normal if the glass went on ringing forever. Here the amplitude of oscillation decays in time, so we call its modes quasi-normal. To a very high degree of accuracy, quasinormal ringing can be approximated by

where is the amplitude of oscillation, is the frequency, and is the decay rate. The quasinormal frequency is described by two numbers,

or, more compactly

where stands for the real part. Here, is what is commonly referred to as the quasinormal mode frequency. It is a complex number with two pieces of information: real part is the temporal oscillation; imaginary part is the temporal, exponential decay.

In certain cases the amplitude of the wave decays quickly, to follow the decay for a longer time one may plot

The sound of quasinormal ringing