Stability of Matter (course webpage)



Where and when: Mondays 15:45-19:00 (room. 2.08)

Lectures/exercises contents (more or less):
  • 27.02.2023: introduction, motivations, definition of stability of first kind, hydrogen atom Notes 1
  • 06.03.2023: Sobolev inequalities in d>2, stability of first kind for non-relativistic systems in dimensions d>2 Notes 2 Notes 3
  • 13.03.2023: Sobolev inequalities in d<3, stability of first kind for non-relativistic systems in dimensions d<3 and pseudorelativistic systems; eigenvalues Notes 4
  • 20.03.2023: CLR bound and the Lieb-Thirring inequality Notes 5
  • 27.03.2023: Lieb-Thirring inequality and semiclassics. Introduction to many-body QM. Slater determinants. Notes 6 Notes 7
  • 03.04.2023: Reduced density matrices. Pauli's exclusion principle. Ideal Fermi gas. Notes 8
  • 17.04.2023: Kinetic Lieb-Thirring for anti-symetric functions. Eletrostatics, Newton's theorem. Notes 9
  • 24.04.2023: Baxter's electrostatc inequality. Stability of second kind. Thermodynamic limit. Notes 10
  • 08.05.2023: Grand canonical stability. Bosonic instablity. Notes 11
  • 15.05.2023: Ionization conjecture. Derivation of Thomas-Fermi theory. Notes 12 Notes 13
  • 22.05.2023: Scaling properties of TF functional. Levy-Lieb functional. Notes 14
  • 29.05.2023: Gamma convergence of Levy-Lieb functional. Notes 15
  • 12.06.2023: Validity of TF theory. Ionization in TH theory. Other effective theories (TFW, TFDW, HF). Notes 16

    • Oral exam: Proposed terms: 19.06 Monday (9-14), 26.06 Monday (9-14), 30.06 Friday (10-14), 03.07 Monday (9-14)
    Examination topics


    Email address: marcin.napiorkowskiINfuw.edu.sk (please replace "IN" by "@" and "sk" by "pl")
    June 2023