Department Mathematik
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Mathematics of Bose-Einstein Condensation WS 2018


Time and place: Tuesday 14.15-15.45, Room B 134

Goal: The goal of the course is to provide an introduction to the mathematical questions and formalism related to Bose–Einstein Condensation.

Literature:
  • [Sei] Robert Seiringer, "Hot topics in cold gases", Japan. J. Math. 8, 185-232 (2013)
  • [LewNamSerSol] M. Lewin, P.T. Nam, S. Serfaty, J.P. Solovej, Bogoliubov spectrum of interacting Bose gasges, Comm. Pure App. Math. 68 (3), 413–471 (2015)
  • [LewNamRou] M. Lewin, P.T. Nam, N. Rougerie: Derivation of Hartreeʼs theory for generic mean-field Bose systems, Advances in Mathematics 254, 570-621 (2014)
  • [NamRouSei] P.T. Nam, N. Rougerie, R. Seiringer: Ground states of large bosonic systems: the Gross–Pitaevskii limit revisited, Analysis & PDE 9 (2), 459-485 (2016)
  • [LieSeiSolYng] E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason: The Mathematics the of Bose gas and its condensation, Birkhäuser
  • [Sol] J.P. Solovej, Many Body Quantum Mechanics, lecture notes

Notes: Notes Part 1, Notes Part 2, Notes Part 3, Notes Part 4 Notes Part 5 Notes Part 6


    Programme (tentative):

    16/10/2018: Introduction; many-body quantum systems; quantities of interest.

    23/10/2018 Fock space formalism and second quantization (based on Chapters 6 and 7 of [Sol])

    30/10/2018 The free Bose gas (based on Chapeter 2.4. in [Sei] and/or any statistical physics textbook)

    6/11/2018 Density and Reduced Density Matrices, the concept of BEC for interacting Bose gases (based on 3.1.4 and 3.1.5 of [LieSei])

    13/11/2018 Hartree and Gross-Pitaevskii theories: an overview (based on the introductions of [LewNamRou] and [NamSeiRou])

    20/11/2018 A non-rigorous primer on Bogoliubov theory (based on appendix A in [LieSeiSolYng])

    27/11/2018 NO SEMINAR

    4/12/2018 Rigorous Bogoliubov theory 1 (up to the formulation of Thm 2.2. in [LewNamSerSol])

    11/12/2018 Rigorous Bogoliubov theory 2: (Chapter 4 in [LewNamSerSol])

    18/12/2018 Rigorous Bogoliubov theory 3: (Chapter 5 in [LewNamSerSol])

    8/1/2019 Rigorous Bogoliubov theory 4: (Chapter 6 in [LewNamSerSol])

    15/1/2019 NO SEMINAR

    22/1/2019 Rigorous Bogoliubov theory 5: (Chapter 7 in [LewNamSerSol])

    29/1/2019 Dynamics of BEC

    05/2/2019 Most recent developements