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 16:04, 19 February 2005 editJag123 (talk | contribs)5,113 editsm ch to {{physics-stub}} - Misplaced Pages:WikiProject Stub sorting← Previous edit Revision as of 00:18, 13 May 2005 edit undo152.2.88.224 (talk)No edit summaryNext edit →
Line 1: Line 1:
==General Definition==
'''Quasinormal modes''' ('''QNM''') are the modes of ] dissipation of a
perturbed object or a field. Consider a familiar example where one
perturbs (gently hits) a wine glass with a knife: the glass begins to
ring, it rings with a set, superposition if you will, of its natural
frequencies -- its modes of sonic ] dissipation. One might be
tempted to call those modes ''normal'', however the glass does not go
on ringing forever, amplitude of oscillation decays in time; we
therefore 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>

where <math>\psi\left(t\right)</math> is the amplitude of oscillation,
<math>\omega^{\prime}</math> is the frequency, and
<math>\omega^{\prime\prime}</math> is the decay rate. Quasinormal
mode, two numebrs, is

:<math>\omega = \left(\omega^{\prime} , \omega^{\prime\prime}\right)</math>

or, more compactly

:<math>\psi\left(t\right) \approx e^{i\omega t}</math>

:<math>\omega =\omega^{\prime} + i\omega^{\prime\prime}</math>

where <math>\psi\left(t\right)</math> stands for the real part. Here,
<math>\mathbf{\omega}</math> is what is commonly referred to as the
'''quasinormal mode'''. It is a ] with two pieces of
information: real part is the temporal oscillation; imaginary part is
the temporal, ].

::]

::]

::'''I'll be back...'''

==Someone else wrote something really confusing...==
In ], a '''quasinormal mode''' is a formal solution of linearized ]s (such as the linearized equations of ] constraining perturbations around a ] solution) with a complex ] (]). In ], a '''quasinormal mode''' is a formal solution of linearized ]s (such as the linearized equations of ] constraining perturbations around a ] solution) with a complex ] (]).


Revision as of 00:18, 13 May 2005

General Definition

Quasinormal modes (QNM) are the modes of energy dissipation of a perturbed object or a field. Consider a familiar example where one perturbs (gently hits) a wine glass with a knife: the glass begins to ring, it rings with a set, superposition if you will, of its natural frequencies -- its modes of sonic energy dissipation. One might be tempted to call those modes normal, however the glass does not go on ringing forever, amplitude of oscillation decays in time; we therefore 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. Quasinormal mode, two numebrs, is

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

or, more compactly

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

where ψ ( t ) {\displaystyle \psi \left(t\right)} stands for the real part. Here, ω {\displaystyle \mathbf {\omega } } is what is commonly referred to as the quasinormal mode. It is a complex number with two pieces of information: real part is the temporal oscillation; imaginary part is the temporal, exponential decay.

File:Qnm.jpg
The sound of quasinormal ringing
I'll be back...

Someone else wrote something really confusing...

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.

See also

Stub icon

This physics-related article is a stub. You can help Misplaced Pages by expanding it.

Category: