Relaxation time

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Relaxation time is a general physics concept for the characteristic time in which a system relaxes under certain changes in external conditions.

[edit] Physics

In physics, relaxation time refers to the time-dependent response of a system to well-defined external stimuli. For instance, the properties of a dielectric change on a time scale determined by the relaxation time when an external electric field is changed (dielectric relaxation).

A property of the solid that is closely related to its conductivity is its dielectric relaxation time. The dielectric relaxation time is a measure of the time it takes for charge in a semiconductor to become neutralized by conduction process. it is small in metals and can be large in semiconductors and insulators.

[edit] Astronomy

In astronomy, relaxation time relates to clusters of gravitationally-interacting bodies (star clusters, galaxy clusters, globular clusters). Various events occur on timescales relating to the relaxation time, including core collapse and energy exchange between stars (minimization of the total energy in a cluster).

The relaxation time is related to the velocity of a body (typically a star) and the perturbation rate. In the example of a star cluster, a particular star will have an orbit with a velocity v. As the star passes by other stars, the orbit will be perturbed by the gravitational field of nearby stars. The relaxation time is similar to the ratio of the velocity to the time derivative of the perturbation.

[edit] Mathematics

Let the homogenous differential equation: $m\frac{d^2 y}{d t^2}+\gamma\frac{d y}{d t}+ky=0$ model damped unforced oscillations of a weight on a spring.

The displacement will then be of the form y(t) = Ae^-t/Tcos(μt - δ). The constant T is called the relaxation time of the system and the constant μ is the quasi-frequency.