Misplaced Pages

Quasinormal mode: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editNext edit →Content deleted Content addedVisualWikitext
Revision as of 11:23, 11 May 2016 editBibcode Bot (talk | contribs)Bots42,789 editsm Adding 1 arxiv eprint(s), 1 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot← Previous edit Revision as of 14:46, 8 August 2016 edit undo77.197.165.114 (talk)No edit summaryTag: Visual editNext edit →
Line 4: Line 4:


==Example== ==Example==
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 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 '']'' 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


:<math>\psi(t) \approx e^{-\omega^{\prime\prime}t}\cos\omega^{\prime}t</math> :<math>\psi(t) \approx e^{-\omega^{\prime\prime}t}\cos\omega^{\prime}t</math>

Revision as of 14:46, 8 August 2016

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "Quasinormal mode" – news · newspapers · books · scholar · JSTOR (July 2009) (Learn how and when to remove this message)

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.

Example

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

ψ ( t ) ≈ e − ω ′ ′ t cos ⁡ ω ′ t {\displaystyle \psi (t)\approx e^{-\omega ^{\prime \prime }t}\cos \omega ^{\prime }t}

where ψ ( t ) {\displaystyle \psi \left(t\right)} is the amplitude of oscillation, ω ′ {\displaystyle \omega ^{\prime }} is the frequency, and ω ′ ′ {\displaystyle \omega ^{\prime \prime }} is the decay rate. The quasinormal frequency is described by two numbers,

ω = ( ω ′ , ω ′ ′ ) {\displaystyle \omega =\left(\omega ^{\prime },\omega ^{\prime \prime }\right)}

or, more compactly

ψ ( t ) ≈ Re ⁡ ( e i ω t ) {\displaystyle \psi \left(t\right)\approx \operatorname {Re} (e^{i\omega t})}
ω = ω ′ + i ω ′ ′ {\displaystyle \omega =\omega ^{\prime }+i\omega ^{\prime \prime }}

Here, ω {\displaystyle \mathbf {\omega } } 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 log ⁡ | ψ ( t ) | {\displaystyle \log \left|\psi (t)\right|}

The sound of quasinormal ringing
Problems playing this file? See media help.

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.

See also

References

  1. Konoplya, R. A.; Zhidenko, Alexander (2011-07-11). "Quasinormal modes of black holes: From astrophysics to string theory". Reviews of Modern Physics. 83 (3): 793–836. arXiv:1102.4014. Bibcode:2011RvMP...83..793K. doi:10.1103/RevModPhys.83.793.
  2. Kokkotas, Kostas D.; Schmidt, Bernd G. (1999-01-01). "Quasi-Normal Modes of Stars and Black Holes". relativity.livingreviews.org. Retrieved 2015-10-29.
Categories: