File:Reaction diffusion target.gif

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Reaction_diffusion_target.gif(265 × 235 pixels, file size: 39 KB, MIME type: image/gif)

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Bloch oscillation is a phenomenon from solid state physics. It describes the oscillation of a particle (e.g. an electron) confined in a periodic potential when a constant force is acting on it. It was first pointed out by Bloch and Zener while studying the electrical properties of crystals. In particular, they predicted that the motion of electrons in a perfect crystal under the action of a constant electric field would be oscillatory instead of uniform. While in natural crystals this phenomenon is extremely hard to observe due to the scattering of electrons by lattice defects, it has been observed in semiconductor superlattices and in different physical systems such as cold atoms in an optical potential and ultrasmall Josephson junctions.

Derivation

The one-dimensional equation of motion for an electron in a constant electric field E is:

,

which has the solution

.

The velocity v of the electron is given by

,

where denotes the dispersion relation for the given energy band. Suppose that the latter has the (tight-binding) form

,

where a is the lattice parameter and A is a constant. Then v(k) is given by

,

and the electron position by

.

This shows that the electron oscillates in real space. The frequency of the oscillations is given by .

See also

Summary

Description
English: Target pattern (numerical calculation) in a two-component reaction-diffusion system of Fitzhugh-Nagumo type, produced by Dr. H. U. Bödeker. The image is a snapshot of a periodically repeating sequence in which the center of the target pattern oscillates while the individual rings propagate from the center to the domain boundary. A finite-element algorithm was used in the calculation.
Date 6 July 2007 (original upload date)
Source Transferred from en.wikipedia to Commons.
Author Huboedeker at English Wikipedia

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Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2007-07-06 09:56 265×235× (40053 bytes) Huboedeker Target pattern (numerical calculation) in a two-component reaction-diffusion system of Fitzhugh-Nagumo type, produced by Dr. H. U. Bödeker.

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Date/TimeThumbnailDimensionsUserComment
current21:33, 18 March 2015Thumbnail for version as of 21:33, 18 March 2015265 × 235 (39 KB)wikimediacommons>BD2412Transferred from en.wikipedia

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