PhD thesis in English

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$Edge excitations of paired fractional quantum Hall states$

2. Diagonalization of Transition Amplitudesy-15-10-5050.040.020-0.02-0.04y-15-10-5050.040.020-0.02-0.04101015-15 -10 -5 0 5 10 15x15-15 -10 -5 0 5 10 15xy-15-10-5050.040.020-0.02-0.04y-15-10-5050.040.020-0.02-0.04101015-15 -10 -5 0 5 10 15x15-15 -10 -5 0 5 10 15xFigure 2.15: Density plots of level k = 1, 2, 3, 4 eigenstates of a d = 2 anharmonicpotential (2.36) obtained using p = 21 effective action. The parameters are k 2 =−0.1025, k 4 = k exp4 , L = 20, ∆ = 0.25, t = 0.2.potential (2.36). Due to the high degeneracy of energy eigenstates in d = 2, thehistogram of numerically found energy levels contains enough statistics over thewhole region of energies, and therefore can be used for assessment of the quality ofnumerical spectra. As we see, the agreement is better and better when we use finerspace discretization. Depending on the needed number of energy levels and maximalvalue of the energy considered to be relevant for the calculation we can chooseappropriate values of discretization parameters that will provide reliable numericalresults up to desired energy value. For example, for the choice of discretizationparameters L = 14, ∆ = 0.14, we can reliably use energy levels up to E ≈ 120.Fig. 2.16(bottom) shows the comparison of cumulative density of states n(E)calculated for numerically obtained results and in semiclassical approximation, by51
2. Diagonalization of Transition Amplitudes250200L = 14.4, ∆ = 0.14L = 14.4, ∆ = 0.24L = 10, ∆ = 0.25L = 5, ∆ = 0.251501005003500030000250000 50 100 150 200 250L = 14.4, ∆ = 0.14L = 14.4, ∆ = 0.24L = 10, ∆ = 0.25L = 5, ∆ = 0.25200001500010000500000 50 100 150 200 250 300Figure 2.16: Distribution of the density of numerically obtained energy eigenstates(top) and cumulative distribution of the density of numerically obtained energyeigenstates (bottom) for a d = 2 anharmonic potential (2.36), calculated with thelevel p = 21 effective action. The parameters are k 2 = 1, k 4 = k exp4 , t = 0.2, whilediscretization parameters are given on the graph, corresponding to the curves topto bottom. Long-dashed lines on both graphs give the corresponding semiclassicalapproximations.integrating the expression (2.38), which can be calculated analytically. The comparisonof numerical and semiclassical cumulative density of states in Fig. 2.16(bottom)verifies our conclusions from Fig. 2.16(top), and again sets the same limit of reliableenergy levels for chosen discretization parameters.52
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UNIVERSITY OF BELGRADEFACULTY OF PH
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Thesis advisor, Committee member:Dr
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lence for Computer Modeling of Comp
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dobijanje kondenzata odabrani su at
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Uticaj slabih interakcija na fenome
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Abstract of the doctoral dissertati
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highly accurate information on ener
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Keywords: cold quantum gases, Bose-
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CONTENTS3.4.2 Time-of-flight graphs
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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
Page 66 and 67: ||2. Diagonalization of Transition
Page 74: 2. Diagonalization of Transition Am
Page 79 and 80: magnetic field ⃗ B = 2M ⃗ Ω.3.
Page 81 and 82: 3. Rotating ideal BECof the rotatio
Page 83 and 84: 3. Rotating ideal BEC3.1 Numerical
Page 85 and 86: 3. Rotating ideal BEC350300SC appro
Page 87 and 88: 3. Rotating ideal BEC3.2 Finite num
Page 89 and 90: 3. Rotating ideal BECN - N 03.0·10
Page 91 and 92: 3. Rotating ideal BEC3.3 Global pro
Page 93 and 94: 3. Rotating ideal BECever, it does
Page 95 and 96: 3. Rotating ideal BECT c [nK]120110
Page 97 and 98: 3. Rotating ideal BEC3.533210 3 κ
Page 99 and 100: 3. Rotating ideal BECn(x, y)10·10
Page 101 and 102: 3. Rotating ideal BECpancy numbers
Page 103 and 104: 3. Rotating ideal BEC6·10 4 0 0.02
Page 105 and 106: Chapter 4Mean-field description of
Page 107 and 108: 4. Mean-field description of an int
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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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