欢迎来到天天文库
浏览记录
ID:39904967
大小:157.66 KB
页数:13页
时间:2019-07-14
《statistics of zeros of Husimi representations of quantum chaotic eigenstates and random polynomials》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、February5,2008ParametricstatisticsofzerosofHusimirepresentationsofquantumchaoticeigenstatesandrandompolynomialsTomaˇzProsen1PhysicsDepartment,FacultyofMathematicsandPhysics,UniversityofLjubljana,Jadranska19,1000Ljubljana,SloveniaAbstractLocalparametricstatisticsofzerosofHusimireprese
2、ntationsofquantumeigen-statesareintroduced.ItisconjecturedthatforaclassicallyfullychaoticsystemsoneshouldusethemodelofparametricstatisticsofcomplexrootsofGaussianrandompoly-nomialswhichisexactlysolvableasdemonstratedbelow.Forexample,thevelocities(derivativesofzerosofHusimifunctionwit
3、hrespecttoanexternalparameter)arepre-dictedtoobeyauniversal(non-Maxwellian)distributiondP(v)222−3=(1+
4、v
5、/σ),dv2πσ2whereσ2isthemeansquarevelocity.Theconjectureisdemonstratednumericallyinagenericchaoticsystemwithtwodegreesoffreedom.Dynamicalformulationofthe“zero–flow”intermsofanintegrab
6、lemany-bodydynamicalsystemisgivenaswell.arXiv:chao-dyn/9612006v13Dec19961IntroductionTheintenseresearchintheso-calledquantumchaologyhasproducedmanydifferentsig-naturesofclassicalchaosinthecorrespondingquantumHamiltoniansystems.Ithasbeenfoundthatenergyspectraandeigenstatesofclassically
7、fullychaoticquantumsys-temshaveuniversalstatisticalpropertieswhichcanbedescribedbystochasticmodelswithnofreeparameters,likerandommatrixtheory(RMT).IntheBargmann(orHusimi)representation,eigenstatesofquantumsystemscanbeuniquelyrepresentedintermsofcomplexanalyticfunctionsinphasespacevar
8、iables.Quiterecently,ithasbeenproposed[7]thatincaseof1-dimsystems(orPoincar´esurface1e-mail:prosen@fiz.uni-lj.si1ofsectionreductionsof2-dimsystems[10]),wherephasespaceistwodimensional,andonehasonlyonecomplexvariablez=q+ip,anyeigenstatecanbeuniquelyrepresentedbythecollectionof(complex)
9、zerosofitsBargmannorHusimirepresentation.Thishasbeencalledthestellarrepresentation.Ithasbeenfound[10]thatthestructureofzerosofHusimirepresentationofaneigenstateisreminiscentofthestructureofclassicalphasespace:(i)inclassicallyfullychaoticsystemsthezerostendtospreaduniformlyoverthewhol
10、eclassically
此文档下载收益归作者所有