11137.有限溫度下一維費(fèi)米氣體集體激發(fā)呼吸模的研究

1、有限溫度下一維費(fèi)米氣體集體激發(fā)呼吸模的研究Collectivebreathingmodeof1DFermigasatfinitetemperature俞玄平XuanpingYu導(dǎo)師：高先龍教授Supervisor：ProfXianlongGao浙江師范大學(xué)物理系DepartmentofPhysicsZhejiangNormalUniversity五月，2016May2016理論物理專業(yè)碩士學(xué)位論文Thesis“10rtheMscDegr

2、eeinTheoreticalPhysicsAbstractInthispaper，weuseNewton’smethodtosolvetheGaudinYangmodelofeoupledthermodynamicBetheansatzequationsinthehomogenoussystemTherelevantthermodynamicpropertiesofthesystemaxeobtainedThebreath—ingmo

3、deofthecollectiveoscillatingfrequencyintheone—dimensionaIharmonlctrapGaudin‘YangmodelWaSobtainedbyusingLandau’stwo—fluidtheoryandvariationalmethodInthefirsttWoehaptersweintroducethebackgroundandsignificanceoftheresearchf

4、orcoldatomsandonedimensionalstronglycorrelatedsystem8，thenweintroducetheb赫cconceptsofcoldatomrelatedresearchandtheprog。e88monedimensionalstronglycorrelatedsystemsbyfollowingotlrresearchcollectiveeXcitationbreathingmodeof

5、1DFermigasatfinitetemperatureAtthefirstaspect，westudythermodynamicpropertiesofGaudinYangm。delatfiniret鋤peratl】reinonedimei_1sionalhomogeneoussystemBYsotvingthethermodynamicBetheansatzequationsusingNewton’smethod7wregetth

6、ethermoaynamicquantities，sucha8densityspecificheat，entropycompressibilityLnttingerDar鋤etersdependingontemperatureandchemicalpotentlalWegetthesvsternsphases，theclassicregime，criticalregimeandthequantumnreglmeTheDhasetrmas

7、itionboundaryareamaybedeterminedbythespecificheatpeaklineAtthesecondaspect，weintroducethebackgroundofexperimentsandthesignificanceofhydrodynamicsmethodforsolvingthecollectiveoscillation8ofone—dimensionalstronglycorrelate

8、dsystem，wegetthebreathingn20de扛equemcvofGaudim、‰lgmodeintheharmonicpotentialbyvariationalmethodD1PolemodefrequencyandbreathingmodefrequencyaxeobtainedWegetthedistrjbutionofDarticlenumberdensitybyusinglocaldensityapproxim