- Topological defect
: "Also see base concepts:
topology ,differential equation s,quantum theory " & "condensed matter physics".Inmathematics andphysics , a topological soliton or a topological defect is a solution of a system ofpartial differential equation s or of aquantum field theory that can be proven to exist because theboundary conditions entail the existence of homotopically distinct solutions. Typically, this occurs because the boundary on which the boundary conditions are specified has a non-trivialhomotopy group which is preserved bydifferential equation s; the solutions to the differential equations are then topologically distinct, and are classified by theirhomotopy class . Topological defects are not only stable against small s, but cannot decay or be undone or be de-tangled, precisely because there is no continuous transformation that will map them (homotopically) to a uniform or "trivial" solution.Examples include the
soliton orsolitary wave which occurs in manyexactly solvable model s, the screw dislocations in crystalline materials, theSkyrmion and theWess-Zumino-Witten model in quantum field theory.Topological defects are believed to drive
phase transition s incondensed matter physics. Notable examples of topological defects are observed inLambda transition universality class systems including: screw/edge-dislocations inliquid crystals ,magnetic flux tube s insuperconductors , vortices insuperfluids .Cosmology
Certain
grand unified theories predict topological defects to have formed in the earlyuniverse . According to theBig Bang theory, the universe cooled from an initial hot, dense state triggering a series of phase transitions much like what happens in condensed-matter systems. Inphysical cosmology , a topological defect is an (often) stable configuration of matter predicted by some theories to form atphase transition s in the very early universe.Symmetry breakdown
Depending on the nature of
Symmetry breakdown , varioussoliton s are believed to have formed in the early universe according to theHiggs-Kibble mechanism . The well-known topological defects aremagnetic monopole s,cosmic string s,domain wall s,Skyrmion s and textures.As the universe expanded and cooled, symmetries in the laws of physics began breaking down in regions that spread at the
speed of light ; topological defects occur where different regions came into contact with each other. The matter in these defects is in the original symmetric phase, which persists after a phase transition to the new asymmetric new phase is completed.Types of topological defects
Various different types of topological defects are possible, with the type of defect formed being determined by the symmetry properties of the matter and the nature of the phase transition. They include:
*
Domain wall s, two-dimensional membranes that form when a discrete symmetry is broken at a phase transition. These walls resemble the walls of a closed-cellfoam , dividing the universe into discrete cells.
*Cosmic string s are one-dimensional lines that form when an axial or cylindrical symmetry is broken.
*Monopoles, point-like defects that form when a spherical symmetry is broken, are predicted to have magnetic charge, either north or south (and so are commonly called "magnetic monopole s").
*Textures form when larger, more complicated symmetry groups are completely broken. They are not as localized as the other defects, and are unstable. Other more complex hybrids of these defect types are also possible.Observation
Topological defects are extremely high-energy phenomena and are likely impossible to produce in artificial Earth-bound physics experiments, but topological defects that formed during the universe's formation could theoretically be observed.
No topological defects of any type have yet been observed by astronomers, however, and certain types are not compatible with current observations; in particular, if domain walls and monopoles were present in the observable universe, they would result in significant deviations from what astronomers can see. Theories that predict the formation of these structures "within the observable universe" (see: "inflation") can therefore be largely ruled out. On the other hand,
cosmic string s have been suggested as providing the initial 'seed'-gravity around which thelarge-scale structure of the cosmos of matter has condensed. Textures are similarly benign. In late 2007, a cold spot in thecosmic microwave background was interpreted as possibly being a sign of a texture lying in that direction. [cite journal| journal=Science| doi=10.1126/science.1148694| title=A Cosmic Microwave Background Feature Consistent with a Cosmic Texture| first=M.| last= Cruz| coauthors= N. Turok, P. Vielva, E. Martínez-González, M. Hobson| url= http://www.sciencemag.org/cgi/content/abstract/1148694| accessdate=2007-10-25| volume=318| pages=1612| year=2007| pmid=17962521]
=ee also
*
quantum vortex
*dislocation References
External links
* [http://www.damtp.cam.ac.uk/user/gr/public/cs_top.html Cosmic Strings & other Topological Defects]
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