Bogoliubov Excitations of Inhomogeneous Bose-Einstein ...

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Bibliography [131] F. Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, Zeitschrift für Physik 52, 555 (1929). [132] C. Zener, Non-adiabatic crossing of energy levels, Proceedings of the Royal Society of London. Series A 137, 696 (1932). [133] —, A theory of the electrical breakdown of solid dielectrics, Proceedings of the Royal Society of London. Series A 145, 523 (1934). [134] J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt- Rink, Optical investigation of Bloch oscillations in a semiconductor superlattice, Phys. Rev. B 46, 7252 (1992). [135] K. Leo, P. H. Bolivar, F. Brüggemann, R. Schwedler, and K. Köhler, Observation of Bloch oscillations in a semiconductor superlattice, Solid State Communications 84, 943 (1992). [136] O. Morsch and M. Oberthaler, Dynamics of Bose-Einstein condensates in optical lattices, Rev. Mod. Phys. 78, 179 (2006). [137] R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Experimental observation of linear and nonlinear optical Bloch oscillations, Phys. Rev. Lett. 83, 4756 (1999). [138] T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Optical Bloch oscillations in temperature tuned waveguide arrays, Phys. Rev. Lett. 83, 4752 (1999). [139] A. Trombettoni and A. Smerzi, Discrete solitons and breathers with dilute Bose-Einstein condensates, Phys. Rev. Lett. 86, 2353 (2001). [140] A. Smerzi and A. Trombettoni, Nonlinear tight-binding approximation for Bose-Einstein condensates in a lattice, Phys. Rev. A 68, 023613 (2003). [141] M. Salerno, V. V. Konotop, and Y. V. Bludov, Long-living Bloch oscillations of matter waves in periodic potentials, Phys. Rev. Lett. 101, 030405 (2008). [142] Y. V. Bludov, V. V. Konotop, and M. Salerno, Long-lived matter wave Bloch oscillations and dynamical localization by time-dependent nonlinearity management, J. Phys. B: At. Mol. Opt. Phys. 42, 105302 (2009). 152
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Page 1:
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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Page 39 and 40:
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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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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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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
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 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 167 and 168: Acknowledgments I thank everybody w
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