Problem Sets:

Literature:

1. History of Bose-Einstein distribution:
   
   
   • M. Delbrück,
     Was Bose-Einstein statistics arrived at by serenipity?,
     J. Chem. Educ. 57, 467 (1980)
     
     
   • Chapter 2 in V.V. Kocharovsky, V.V. Kocharovsky, M. Holthaus, C.H.R. Ooi, A. Svidzinsky, W. Ketterle, and M.O. Scully,
     Fluctuations in Ideal and Interacting Bose-Einstein Condensates: From the Laser Phase Transition Analogy to Squeezed States and Bogoliubov Quasiparticles,
     in G. Rempe and M.O. Scully (Eds.), Advances in Atomic, Molecular, and Optical Physics, Vol. 53, Academic Press, 2006, p. 293
   
   
2. Introduction in Bose-Einstein Condensation, Cooling Techniques:
   
   
   • Chapter 1 and 4 in C.J. Pethick and H. Smith,
     Bose-Einstein Condensation in Dilute Gases,
     Second Edition, Cambridge University Press (2008)
   
   
3. Ideal Bose-Gas, Grand-Canonical Ensemble:
   
   
   • Chapter 2 in C.J. Pethick and H. Smith,
     Bose-Einstein Condensation in Dilute Gases,
     Second Edition, Cambridge University Press (2008)
     
     
   • B. Klünder and A. Pelster,
     Systematic Semiclassical Expansion for Harmonically Trapped Ideal Bose Gases,
     Europ. Phys. J. B 68, 457 (2009)
   
   
4. Ideal Bose-Gas, Canonical Ensemble:
   
   
   • M. Holthaus, E. Kalinowski, and K. Kirsten,
     Condensate fluctuations in trapped Bose gases: Canonical vs. microcanonical ensemble,
     Ann. Phys. (N.Y.) 270, 198 (1998)
     
     
   • M. Holthaus and E. Kalinowski,
     Universal renormalization of saddle-point integrals for condensed Bose gases,
     Phys. Rev. E 60, 6534 (1999)
     
     
   • K. Glaum, H. Kleinert, and A. Pelster,
     Condensation of Ideal Bose Gas Confined in a Box within a Canonical Ensemble,
     Phys. Rev. A 76, 063604 (2007)
     
     
   • Chapter 7 in H. Kleinert,
     Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets,
     Fifth Edition, World Scientific (2009)
     
     
   
   
5. Scattering Theory:
   
   
   • Chapter 5 until Section 5.2 in C.J. Pethick and H. Smith,
     Bose-Einstein Condensation in Dilute Gases,
     Second Edition, Cambridge University Press (2008)
     
     
   • Chapter 5 in A. Pelster,
     Bose-Einstein-Kondensation,
     Vorlesungsmanuskript (2004)
   
   
6. Gross-Pitaevskii Equation, Thomas-Fermi Approximation:
   
   
   • Chapter 6 in C.J. Pethick and H. Smith,
     Bose-Einstein Condensation in Dilute Gases,
     Second Edition, Cambridge University Press (2008)
   
   
7. Eigenfrequencies of a Condensate:
   
   
   • V.M. Perez-Garcia, H. Michinel, J.I. Cirac, M. Lewenstein, and P. Zoller,
     Low Energy Excitations of a Bose-Einstein Condensate: A Time-Dependent Variational Analysis,
     Phys. Rev. Lett. 77, 5320 (1996))
     
     
   • V.M. Perez-Garcia, H. Michinel, J.I. Cirac, M. Lewenstein, and P. Zoller,
     Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations,
     Phys. Rev. A 56, 1424 (1997)
     
     
   • M. Herold,
     Sum-Rule Approach for Collective Excitations of Ultracold Quantum Gases,
     Bachelor Thesis, Freie Universität Berlin (2012)
   
   
8. Hartree-Fock Theory:
   
   
   • Öhberg and S. Stenholm,
     A Hartree - Fock study of a Bose condensed gas,
     J. Phys. B 30, 2749 (1997)
   
   
9. Shift of Cricital Temperature:
   
   
   • S. Giorgini, L. P. Pitaevskii, and S. Stringari,
     Condensate fraction and critical temperature of a trapped interacting Bose gas,
     Phys. Rev. A 54, R4633 (1996)
     
     
   • F. Gerbier, J. H. Thywissen, S. Richard, M. Hugbart, P. Bouyer, and A. Aspect,
     Critical Temperature of a Trapped, Weakly Interacting Bose Gas,
     Phys. Rev. Lett. 92, 030405 (2004)
   
   
10. Bogoliubov Theory:
    
    
    • Chapter 8 until Section 8.1.4 in C.J. Pethick and H. Smith,
      Bose-Einstein Condensation in Dilute Gases,
      Second Edition, Cambridge University Press (2008)
    
    
11. Vortices:
    
    
    • Chapter 9 in C.J. Pethick and H. Smith,
      Bose-Einstein Condensation in Dilute Gases,
      Second Edition, Cambridge University Press (2008)
    
    
12. Superfluidity and Landau-Khalatnikov Two-Fluid Model:
    
    
    • Section 10.1 and 10.2 in C.J. Pethick and H. Smith,
      Bose-Einstein Condensation in Dilute Gases,
      Second Edition, Cambridge University Press (2008)
      
      
    • Chapter 2 in C. Wille,
      Hydrodynamic Theory of Ultracold Quantum Gases,
      Bachelor Thesis, Freie Universität Berlin (2011)
    
    
13. Spinor Bose Gases:
    
    
    • Chapter 5, 6, 9, 10 and Appendix D in P. Soltan-Panahi,
      Thermodynamic Properties of F=1 Spinor Bose-Einstein Condensates,
      Diploma Thesis, Freie Universität Berlin (2006)
    
    
14. Disorder:
    
    
    • M. von Hase,
      Bose-Einstein Condensation in Weak and Strong Disorder Potentials,
      Bachelor Thesis, Freie Universität Berlin (2010)
    
    
15. Introduction to Fermi Gases:
    
    
    • Section I-III in S. Giorgini, L.P. Pitaevskii, and S. Stringari,
      Theory of ultracold atomic Fermi gases,
      Rev. Mod. Phys. 80, 1215 (2008)
    
    
16. BEC-BCS-Crossover:
    
    
    • Section V in S. Giorgini, L.P. Pitaevskii, and S. Stringari,
      Theory of ultracold atomic Fermi gases,
      Rev. Mod. Phys. 80, 1215 (2008)
    
    
17. Bosons in Optical Lattices:
    
    
    • Chapter 2 and 3 in A. Hoffmann,
      Bosonen in Optischen Gittern,
      Diplomarbeit, Freie Universität Berlin (2007)
    
    
18. Periodically Driven Optical Lattices:
    
    
    • A. Eckardt, C. Weiss, and M. Holthaus,
      Superfluid-insulator transition in a periodically driven optical lattice,
      Phys. Rev. Lett. 95, 260404 (2005)
      
      
    • A. Eckardt, M. Holthaus, H. Lignier, A. Zenesini, D. Ciampini, O. Morsch, and E. Arimondo,
      Exploring dynamic localization with a Bose-Einstein condensate,
      Phys. Rev. A 79, 013611 (2009)
      
      
    • A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimondo,
      Coherent control of dressed matter waves,
      Phys. Rev. Lett. 102, 100403 (2009)
      
      
    • J. Struck, C. Ölschläger, R. Le Targat, P. Soltan-Panahi, A. Eckardt, M. Lewenstein, P. Windpassinger, and K. Sengstock,
      Quantum simulation of frustrated classical magnetism in triangular optical lattices,
      Science 333, 996 (2011)