Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...

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Bibliography [35] M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond, Adv. Phys. 56, 243 (2007), arXiv:condmat/0606771. [36] I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008). [37] M. Greiner and S. Folling, Condensed-matter physics: Optical lattices, Nature 453, 736 (2008). [38] M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198 (1995). [39] R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, Optical dipole traps for neutral atoms, Advances in Atomic, Molecular, and Optical Physics 42, 95 (2000), preprint: arXiv:physics/9902072. [40] M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, Control of interaction-induced dephasing of Bloch oscillations, Phys. Rev. Lett. 100, 080404 (2008). [41] T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Dynamics of Bloch oscillations in disordered lattice potentials, Phys. Rev. A 77, 023610 (2008). [42] A. Görlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson, J. R. Abo-Shaeer, A. P. Chikkatur, S. Gupta, S. Inouye, T. Rosenband, and W. Ketterle, Realization of Bose-Einstein condensates in lower dimensions, Phys. Rev. Lett. 87, 130402 (2001). [43] E. Tiesinga, B. J. Verhaar, and H. T. C. Stoof, Threshold and resonance phenomena in ultracold ground-state collisions, Phys. Rev. A 47, 4114 (1993). [44] E. Timmermans, P. Tommasini, M. Hussein, and A. Kerman, Feshbach resonances in atomic Bose-Einstein condensates, Physics Reports 315, 199 (1999). [45] T. Köhler, K. Góral, and P. S. Julienne, Production of cold molecules via magnetically tunable Feshbach resonances, Rev. Mod. Phys. 78, 1311 (2006). 144
Bibliography [46] C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, arXiv:0812.1496 (2008). [47] S. N. Bose, Plancks Gesetz und Lichtquantenhypothese, Zeitschrift für Physik A Hadrons and Nuclei 26, 178 (1924). [48] A. Einstein, Quantentheorie des einatomigen idealen Gases, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1924) p. 261; Zweite Abhandlung (1925) p. 3. [49] A. Griffin, Excitations in a Bose-Condensed Liquid, Cambridge Univ. Press (1993). [50] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Microscopic theory of superconductivity, Phys. Rev. 106, 162 (1957). [51] K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75, 3969 (1995). [52] C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett. 75, 1687 (1995). [53] D. G. Fried, T. C. Killian, L. Willmann, D. Landhuis, S. C. Moss, D. Kleppner, and T. J. Greytak, Bose-Einstein condensation of atomic hydrogen, Phys. Rev. Lett. 81, 3811 (1998). [54] C. J. Pethick and H. Smith, Bose-Einstein condensation in dilute gases, Cambridge Univ. Press (2002). [55] L. Pitaevskii and S. Stringari, Bose-Einstein condensation, Clarendon Press, Oxford (2003). [56] C. Raman, M. Köhl, R. Onofrio, D. S. Durfee, C. E. Kuklewicz, Z. Hadzibabic, and W. Ketterle, Evidence for a critical velocity in a Bose-Einstein condensed gas, Phys. Rev. Lett. 83, 2502 (1999). [57] M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Propagation of sound in a Bose-Einstein condensate, Phys. Rev. Lett. 79, 553 (1997), [Erratum: Phys. Rev. Lett. 80, 2967 (1998)]. 145
Page 1:
Bogoliubov Excitations of Inhomogen
Page 5:
Abstract In this thesis, different
Page 8 and 9:
Contents 2.5. Exact diagonalization
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Contents Bibliography 141 List of F
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1. Interacting Bose Gases—Complex
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1.2. Disorder 1.2. Disorder Idealiz
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1.4. Cold-atoms—Universal model s
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1.5. Cold atoms—History and key e
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1.5. Cold atoms—History and key e
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1.6. Standing of this work are rest
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1.6. Standing of this work The disc
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2. The Inhomogeneous Bogoliubov Ham
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2.1. Bose-Einstein condensation of
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2.1. Bose-Einstein condensation of
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2.2. Interacting BEC and Gross-Pita
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Page 39 and 40:
Page 41 and 42:
n(x) n∞ 1 0.8 0.6 0.4 0.2 0 -3 -2
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2.3. Bogoliubov Excitations and pha
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2.3. Bogoliubov Excitations At high
Page 47 and 48:
„ Φq ′ ¯Φ q ′ « V „ Φq
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(2) k ′ q k = ξ2 � k ′′2 +
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k k ′ 2.4.1. Single scattering se
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2.4. Single scattering event back a
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k + − w (1) k ′ k (a) 2.4. Sing
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2.4. Single scattering event theory
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T 1 B 2 2.5. Exact diagonalization
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2.5. Exact diagonalization of the B
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Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
3. Disorder In the previous chapter
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3.1.1. Speckle amplitude 3.1. Optic
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3.1. Optical speckle potential In c
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3.2. A suitable basis for the disor
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3.2. A suitable basis for the disor
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3.3. Effective medium and diagramma
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Page 83 and 84:
Page 85 and 86:
3.4. Deriving physical quantities f
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3.4. Deriving physical quantities f
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Fixed particle number 3.4. Deriving
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ρµξ d 0.2 0.15 0.1 0.05 1 2 3 4
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4. Disorder—Results and Limiting
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4.1. Hydrodynamic limit I: ξ = 0 t
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4.1. Hydrodynamic limit I: ξ = 0 T
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4.1. Hydrodynamic limit I: ξ = 0 I
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ǫk 0.25 0.5 0.75 1 1.25 1.5 1.75 k
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gd(κ) v 2 1.75 1.5 1.25 1 0.75 0.5
Page 105 and 106: 4.2. Hydrodynamic limit II: towards
Page 107 and 108: ∆ǫk ǫk �0.1 �0.2 �0.3 �
Page 109 and 110: 1 0.5 0 -0.5 0 20 40 60 80 100 x/σ
Page 111 and 112: ΛN �0.1 �0.2 �0.3 �0.4 4.3
Page 113 and 114: nnc(V )−nnc(0) nnc(0) 1.2 1.15 1.
Page 115 and 116: 4.4. Particle regime which coincide
Page 117 and 118: 4.4. Particle regime regime, becaus
Page 119 and 120: 0.02 0.015 0.01 0.005 MSg 0.01 0.1
Page 121 and 122: 5. Conclusions and Outlook (Part I)
Page 123 and 124: 5.3. Theoretical outlook potential.
Page 125: Part II. Bloch Oscillations 113
Page 128 and 129: 6. Bloch Oscillations and Time-Depe
Page 146 and 147: λTB t/TB 0.15 0.05 70 60 50 40 30
Page 150 and 151: A. List of Symbols and Abbreviation
Page 152 and 153: 140 A. List of Symbols and Abbrevia
Page 154 and 155: Bibliography [11] P. A. Lee and T.
Page 158 and 159: Bibliography [58] J. Stenger, S. In
Page 160 and 161: Bibliography [81] V. I. Yukalov and
Page 162 and 163: Bibliography [108] A. Mostafazadeh,
Page 164 and 165: Bibliography [131] F. Bloch, Über
Page 167 and 168: Acknowledgments I thank everybody w
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