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| '''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.
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| ==Example==
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| 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
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| :<math>\psi(t) \approx e^{-\omega^{\prime\prime}t}\cos\omega^{\prime}t</math>
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| where <math>\psi\left(t\right)</math> is the amplitude of oscillation,
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| <math>\omega^{\prime}</math> is the frequency, and
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| <math>\omega^{\prime\prime}</math> is the decay rate. The quasinormal
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| frequency is described by two numbers,
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| :<math>\omega = \left(\omega^{\prime} , \omega^{\prime\prime}\right)</math>
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| or, more compactly
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| :<math>\psi\left(t\right) \approx \operatorname{Re}(e^{i\omega t})</math>
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| :<math>\omega =\omega^{\prime} + i\omega^{\prime\prime}</math>
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| Here, <math>\mathbf{\omega}</math> is what is commonly referred to as the
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| '''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]]. | |
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| ::<!-- Deleted image removed: [[Image:qnm.jpg]] -->
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| In certain cases the amplitude of the wave decays quickly, to follow the decay for a longer time one may plot <math>\log\left|\psi(t)\right|</math>
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| ::<!-- Deleted image removed: [[Image:log(abs(qnm)).jpg]] -->
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| {{listen |filename=qnm.ogg |title=The sound of quasinormal ringing |description=}}
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| ==Mathematical Physics==
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| In [[theoretical physics]], a '''quasinormal mode''' is a formal solution of linearized [[differential equation]]s (such as the linearized equations of [[general relativity]] constraining perturbations around a [[black hole]] solution) with a complex [[eigenvalue]] ([[frequency]]).
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| [[Black hole]]s 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.
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| 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.
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| ==Biophysics==
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| In computational biophysics, quasinormal modes, also called quasiharmonic modes, are derived from diagonalizing the matrix of equal-time correlations of atomic fluctuations.
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|
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| ==References==
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| [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=308423 quasinormal modes in the context of the AdS/CFT correspondence] | |
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| ==See also==
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| * [[Resonance (quantum field theory)]].
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| [[Category:Theoretical physics]]
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| [[Category:Waves]]
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| [[Category:Biophysics]]
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