http://www.world-science.net/othernews/100107_goldenratio wrote:âGolden ratioâ hints at hidden atomic symmetryA hithÂerÂto unÂdisÂcovÂered symÂmeÂtry can be found in solÂid matÂter at very small scales, physÂiÂcists are reÂportÂing. The symÂmeÂtry, they say, inÂvolves the goldÂen raÂtio faÂmous from art and arÂchiÂtecÂture.
ParÂtÂiÂcles at the atomÂic, or quanÂtum, scale beÂhave in unÂexÂpected and seemÂingly irraÂtÂional ways. New propÂerÂties emerge that stem from an efÂfect known as HeiÂsenÂbergâs UnÂcerÂtainÂty PrinÂciÂple.
The reÂsearchÂers in the new study foÂcused on the magÂnetÂic maÂteÂriÂal coÂbalt nioÂbate. It conÂsists of linked magÂnetÂic atÂoms, which form chains like a very thin baÂr magÂnet, but only one atÂom wide. They are conÂsidÂered a useÂful modÂel for deÂscribÂing magÂnetism at tiÂny scales in solÂid state matÂter.
When a magÂnetÂic field is apÂplied to the chain at right anÂgles to an aligned âspinâ of its parÂtÂiÂcles, the magÂnetÂic chain transÂforms inÂto a new state called quanÂtum critÂiÂcal, acÂcordÂing to the physÂiÂcists. This can be thought of as a quanÂtum verÂsion of a fracÂtal patÂtern, a patÂtern that looks the same at any scale.
Such a state is alÂso a type of âquanÂtum unÂcerÂtainâ or âSchrödinger catâ state, in which cerÂtain propÂerÂties of the parÂtÂiÂcles are inÂdeÂterÂmiÂnate, said AlÂan TenÂnant of the HelmÂholtz CenÂter BerÂlin for MaÂteÂriÂals and EnÂerÂgy, one of the reÂsearchÂers.
By tunÂing the sysÂtem the reÂsearchÂers found that the chain of atÂoms acts like a guiÂtar string whose tenÂsion comes from inÂterÂacÂtion beÂtween the spins of the conÂstitÂuÂent parÂtÂiÂcles. âFor these inÂterÂacÂtions we found a seÂries,â or âscale,â of âresÂoÂnant notes,â said Radu Coldea of OxÂford UniÂversÂity, who led the reÂsearch.
âThe first two notes show a perÂfect relaÂtÂionÂship with each othÂer,â added ColÂdea, prinÂciÂple auÂthor of a paÂper on the findÂings to apÂpear in the Jan. 8 isÂsue of the reÂsearch jourÂnal SciÂence.
The âpitchâ of these notes, or their freÂquenÂcies of vibraÂtÂion, are in a raÂtio of about 1.618, the same âthe goldÂen raÂtio faÂmous from art and arÂchiÂtecÂture,â he conÂtinÂued. If two numÂbers are reÂlatÂed by the goldÂen raÂtio, their sum is alÂso reÂlatÂed to the largÂer of them by the goldÂen raÂtio. In othÂer words, if A diÂvidÂed by B is that speÂcial numÂber, then A+B diÂvidÂed by A is the same numÂber.
Artists and arÂchiÂtects have have used the goldÂen raÂtio for cenÂturiesâfor exÂamÂple, rectanÂgles 1.618 times highÂer than they are wideâbeÂcause it supÂposedly proÂvides esÂthetÂicÂally pleasÂing forms. The goldÂen raÂtio is irraÂtÂional, like pi, meanÂing its decÂiÂmals go on forÂevÂer.
In the âquanÂtum unÂcerÂtainâ state of matÂter, the raÂtio âreÂflects a beauÂtiÂful propÂerÂty of the quanÂtum sysÂtem â a hidÂden symÂmeÂtry,â ColÂdea said. It is âacÂtually quite a speÂcial one called E8 by mathÂeÂmatiÂcians, and this is its first obÂservaÂtÂion in a maÂteÂriÂal.â The findÂings draÂmatÂicÂally ilÂlusÂtrate how mathÂeÂmatÂiÂcal theÂoÂries deÂvelÂoped for parÂtÂiÂcle physÂics may find apÂplicaÂtÂion in sciÂence at the nanoÂscaleâthe scale of a few atÂomsâand ulÂtiÂmately in fuÂture techÂnolÂoÂgy, he added.
âSuch disÂcovÂerÂies are leadÂing physÂiÂcists to specÂuÂlate that the quanÂtum, atomÂic- scale world may have its own unÂderÂlyÂing orÂder,â said TenÂnant. âSiÂmÂiÂlar surÂprises may await reÂsearchÂers in othÂer maÂteÂriÂals in the quanÂtum critÂiÂcal state.â
The reÂsearchÂers reached their reÂsults by usÂing a speÂcial probe called neuÂtron scatÂterÂing that alÂlows physÂiÂcists to see the atomÂic-scale vibraÂtÂions of a sysÂtem. âUsÂing neuÂtron scatÂterÂing gives us unÂriÂvalled inÂsight inÂto how difÂferÂent the quanÂtum world can be from the everyÂday,â said reÂsearcher Elisa WheelÂer, who has worked at both OxÂford and the BerÂlin cenÂter on the projÂect.
