Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...

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Acknowledgments I thank everybody who contributed to the success <strong>of</strong> this work! I thank my supervisor Cord Axel Müller for good advice, helpful and interesting discussions, simply for a great time! Thanks for a very active time with lots <strong>of</strong> conferences, summer schools and research stays in France and Spain. Besonderer Dank gilt Frau Glas, die stets dafür sorgt, dass der Laden läuft, und die uns allen den Rücken freihält! Ich danke allen meinen Freunden in Bayreuth, die meine Zeit hier erst lebenswert gemacht haben. Besonders genannt seien meine langjährigen Wegbegleiter Jana Schäferhans und Katharina Palmer. Ich danke Martin Aicham, Christopher Groh und der ganzen Mountainbike- Hochschulgruppe für den sportlichen Ausgleich zum Alltag in der Physik. Ich danke meinen Freunden aus meinen ersten Jahren in Bayreuth, die schon lange aus Bayreuth weggezogen sind für eine schöne Zeit. Besonders genannt seien Constantin Gaul, Christian Brunhuber, Jochen Endrejat . . . I thank Rodrigo Lima for providing me some C-code samples that helped me getting started with the numerical work. Ich danke allen, die mich in den letzten Wochen ertragen und unterstützt haben. Allen, die mich extra nicht angerufen haben und trotzdem an mich gedacht haben. Allen, die mir in irgendeiner Weise den Rücken freigehalten haben. Dank an Christopher Groh und Katharina Palmer fürs Korrekturlesen! Dank geht an die Deutsche Forschungsgemeinschaft (DGF) für die Finanzierung meines Forschungsprojektes. I thank everyone involved in the Bloch project: Elena Díaz Garcia, Rodrigo P. A. Lima, Francisco Domínguez-Adame and Cord A. Müller! It was great fun working and spending time with you! 155
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Bogoliubov Excitations of Inhomogen
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Abstract In this thesis, different
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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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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
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„ 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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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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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
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4.2. Hydrodynamic limit II: towards
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∆ǫk ǫk �0.1 �0.2 �0.3 �
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1 0.5 0 -0.5 0 20 40 60 80 100 x/σ
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ΛN �0.1 �0.2 �0.3 �0.4 4.3
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nnc(V )−nnc(0) nnc(0) 1.2 1.15 1.
Page 115 and 116: 4.4. Particle regime which coincide
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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 156 and 157: Bibliography [35] M. Lewenstein, A.
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 168: Thanks to DAAD and Institut d’Opt
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