PhD thesis in English

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$Edge excitations of paired fractional quantum Hall states$

Keywords: cold quantum gases, Bose-Einstein condensation, effectiveaction, exact diagonalization, perturbation theory, nonlinear dynamicsField of Science: PhysicsResearch Area: Condensed matter physicsUDC number: 538.9
ContentsNomenclaturexviii1 Introduction 11.1 Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Few basic facts on Bose-Einstein condensation . . . . . . . . . . . . . 31.2.1 Noninteracting bosonic gas in the harmonic trap . . . . . . . . 31.2.2 Experimental realization . . . . . . . . . . . . . . . . . . . . . 91.2.3 Interacting bosons at low temperatures . . . . . . . . . . . . . 131.3 This thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Properties of quantum systems viadiagonalization of transition amplitudes 192.1 Space-discretized Schrödinger equation . . . . . . . . . . . . . . . . . 222.2 Discretization effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 Effective actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Numerical results for one-dimensional models . . . . . . . . . . . . . 362.5 Numerical results for two-dimensional models . . . . . . . . . . . . . 472.6 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . 553 Thermodynamics of a rotating ideal BEC 573.1 Numerical calculation of energy eigenvalues and eigenstates . . . . . . 623.2 Finite number of energy eigenvalues and semiclassical corrections . . 663.3 Global properties of rotating BECs . . . . . . . . . . . . . . . . . . . 703.3.1 Condensation temperature . . . . . . . . . . . . . . . . . . . . 703.3.2 Ground-state occupancy . . . . . . . . . . . . . . . . . . . . . 743.3.3 Comparison with semiclassical approximation . . . . . . . . . 753.4 Local properties of rotating BECs . . . . . . . . . . . . . . . . . . . . 773.4.1 Density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . 77xv
Page 1 and 2: UNIVERSITY OF BELGRADEFACULTY OF PH
Page 3 and 4: Thesis advisor, Committee member:Dr
Page 6 and 7: lence for Computer Modeling of Comp
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 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
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2. Diagonalization of Transition Am
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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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