Quasinormal mode

Quasinormal mode

=Wave Mechanics=

Quasinormal modes (QNM) are the modes of energy dissipation of aperturbed object or field. A familiar example is theperturbation (gentle tap) of a wine glass with a knife: the glass begins toring, it rings with a set, or superposition, of its naturalfrequencies -- 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 ofaccuracy, quasinormal ringing can be approximated by

:psi(t) approx e^{-omega^{primeprime}t}cosomega^{prime}t

where psileft(t ight) is the amplitude of oscillation,omega^{prime} is the frequency, andomega^{primeprime} is the decay rate. The quasinormalfrequency is described by two numbers,

:omega = left(omega^{prime} , omega^{primeprime} ight)

or, more compactly

:psileft(t ight) approx e^{iomega t}

:omega =omega^{prime} + iomega^{primeprime}

where psileft(t ight) stands for the real part. Here,mathbf{omega} is what is commonly referred to as thequasinormal mode frequency. It is a complex number with two pieces ofinformation: real part is the temporal oscillation; imaginary part isthe temporal, exponential decay.

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In certain cases the amplitude of the wave decays quickly, to follow the decay fora longer time one may plot logleft|psi(t) ight|

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Mathematical Physics

In theoretical physics, a quasinormal mode is a formal solution of linearized differential equations (such as the linearized equations of general relativity constraining perturbations around a black hole solution) with a complex eigenvalue (frequency).

Black holes have many quasinormal modes (also: ringing modes) that describe the exponential decrease of asymmetry of the black hole in time as it evolves towards the perfect spherical shape.

Recently, the properties of quasinormal modes have been tested in the context of the AdS/CFT correspondence. Also, the asymptotic behavior of quasinormal modes was proposed to be related to the Immirzi parameter in loop quantum gravity, but convincing arguments have not been found yet.

Biophysics

In computational biophysics, quasinormal modes, also called quasiharmonic modes, are derived from diagonalizing the matrix of equal-time correlations of atomic fluctuations.

References

[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=308423 quasinormal modes in the context of the AdS/CFT correspondence]

ee also

* resonance (quantum field theory).


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