PhD thesis in English

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$Edge excitations of paired fractional quantum Hall states$

lence for Computer Modeling of Complex Systems). Numerical simulationswere run on the AEGIS e-Infrastructure, supported in part by theEuropean Commission under EU FP7 projects PRACE-1IP, HP-SEEand EGI-InSPIRE.Finally, I am indebted to my mother, sister and Borislav for their unwaveringsupport that goes far beyond my graduate studies.
Rezime doktorske disertacijeNumeričko proučavanje kvantnih gasovana niskim temperaturamaKoncept Boze-Ajnštajn kondenzacije je u fizici prisutan još od 1924. godine, kadaje prvi put uvedena Boze-Ajnštajn statistika za identične čestice celobrojnog spina[1, 2]. Već prva teorijska kvantno-mehanička razmatranja sistema neinteragujućihčestica su ukazala na mogućnost postojanja ovog fenomena. Poznato je da fizičkeosobine atomskih gasova jako zavise od temperature. Na sobnim temperaturama,osobine ovih sistema su dobro opisane zakonima klasične statističke fizike i kvantnifenomeni prolaze neopaženo. Snižavanjem temperature talasna dužina de Broljijevihtalasa materije raste i dolazi do preklapanja talasa koji odgovaraju različitimčesticama. U tom slučaju, kvantna statistika preuzima presudnu ulogu za fizičke osobinesistema. Česticama sa celobrojnim spinom, bozonima, zakoni kvantne statistikedozvoljavaju naseljavanje istog jednočestičnog kvantnog stanja. Kako snižavamotemperaturu, sistem teži konfiguraciji sa minimalnom energijom, a za bozone to jeupravo makroskopski naseljeno osnovno kvantno stanje. Na taj način ovo kvantnostanje postaje dominantno, pa govorimo o makroskopskom kvantnom fenomenu irazlikujemo fazu sa makroskopskom naseljenošću osnovnog stanja (Boze-Ajnštajnkondenzat) i fazu bez ovog svojstava, koju nazivamo normalni gas. Fazni prelazizmedu ove dve faze naziva se Boze-Ajnštajn kondenzacija. I pored jake utemeljenostiteorijskog koncepta, do prve eksperimentalne realizacije ovog faznog prelaza jedošlo tek 1995. godine, a rezultat je nagraden Nobelovom nagradom za fiziku 2001.Kao što smo ukratko objasnili, osnovni pojmovi o fenomenu Boze-Ajnštajn kondenzacijesu uvedeni korišćenjem modela neinteragujućeg gasa. U realnim gasovimaje naravno nemoguće zanemariti interakcije, zbog kojih oni na veoma niskim temperaturamaprelaze u tečno ili čvrsto stanje. Zbog toga je za eksperimentalno postizanjeBoze-Ajnštajn faznog prelaza neophodno koristiti slabo interagujuće gasove,kao što su su, na primer, razredeni gasovi koji interaguju kratkodometnom, Vander-Valsovominterakcijom. U takvom sistemu, u kom je srednje rastojanje izmedučestica veliko zbog male gustine, kvantni fenomeni dolaze do izražaja tek na veomaniskim temperaturama. Zbog mogućnosti efikasnog hladenja, za eksperimentalno
Page 1 and 2: UNIVERSITY OF BELGRADEFACULTY OF PH
Page 3 and 4: Thesis advisor, Committee member:Dr
Page 8 and 9: dobijanje kondenzata odabrani su at
Page 10 and 11: Uticaj slabih interakcija na fenome
Page 12 and 13: Abstract of the doctoral dissertati
Page 14 and 15: highly accurate information on ener
Page 16 and 17: Keywords: cold quantum gases, Bose-
Page 18 and 19: CONTENTS3.4.2 Time-of-flight graphs
Page 20 and 21: NomenclatureRoman Symbolsagk BLMNn(
Page 22 and 23: Chapter 1Introduction1.1 ForewordTh
Page 24 and 25: ently explored to illustrate the ve
Page 26 and 27: Summations in the last expression c
Page 28 and 29: Figure 1.1: The hallmark of the Bos
Page 30 and 31: we discuss in some detail the exper
Page 32 and 33: In the first papers [3, 4], the TOF
Page 34 and 35: where a BG is the off-resonant scat
Page 36 and 37: system given by( ) ǫ Bog ⃗k =
Page 38 and 39: Having the efficient numerical meth
Page 40 and 41: Chapter 2Properties of quantum syst
Page 42 and 43: 2. Diagonalization of Transition Am
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2. Diagonalization of Transition Am
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||2. Diagonalization of Transition
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magnetic field ⃗ B = 2M ⃗ Ω.3.
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3. Rotating ideal BECof the rotatio
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3. Rotating ideal BEC3.1 Numerical
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3. Rotating ideal BEC350300SC appro
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3. Rotating ideal BEC3.2 Finite num
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3. Rotating ideal BECN - N 03.0·10
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3. Rotating ideal BEC3.3 Global pro
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3. Rotating ideal BECever, it does
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3. Rotating ideal BECT c [nK]120110
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3. Rotating ideal BEC3.533210 3 κ
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3. Rotating ideal BECn(x, y)10·10
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3. Rotating ideal BECpancy numbers
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3. Rotating ideal BEC6·10 4 0 0.02
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Chapter 4Mean-field description of
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4. Mean-field description of an int
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Chapter 5Nonlinear BEC dynamics by
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5. BEC excitation by modulation of
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where n = 1, 2, 3, . . . is an inte
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Chapter 6SummarySince the first exp
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short-range interactions.The excita
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of the ground state. Imaginary-time
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(A.13). With another boundary condi
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Appendix B Time-dependent variation
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List of papers by Ivana VidanovićT
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References[1] S. N. Bose, Plancks g
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REFERENCES[21] W. Ketterle, D. S. D
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REFERENCES[45] A. Bogojević, A. Ba
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REFERENCES[70] M. R. Matthews, B. P
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REFERENCES[94] M.-O. Mewes, M. R. A
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REFERENCES[116] K. Staliunas, S. Lo
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CURRICULUM VITAE - Ivana Vidanović
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PhD thesis in English

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