Niels Benedikter

Upcoming Talks
  • Seminar in Lyon, 15 November 2024
  • Seminar at IST Austria, 19 November 2024
  • Mathematical Challenges in Quantum Mechanics, school and workshop, GSSI L'Aquila, 10-14 February 2025
  • Quantum Mathematics at PoliMi, Milano, 26-30 May 2025
  • Emergent phenomena in many-body quantum systems, CIRM Luminy, 8-12 December 2025
Past Scientific Talks

Fermi Liquid and Luttinger Liquid:

  • European Congress of Mathematics, Mini-Symposium "Collective Phenomena of Fermionic Systems", Seville, 15-19 July 2024
  • XXI International Congress On Mathematical Physics, Strasbourg, contributed talk, 1-6 July 2024
  • One World IAMP Mathematical Physics Seminar, online, 4 June 2024
    recorded talk on youtube
  • Conference on Quantum Statistical Mechanics, Toulouse Mathematics Institute, 27-31 May 2024

Describing Quantum Correlations in the Fermi Liquid by Bosonization.

  • Seminar at University of Bologna, 20 March 2024
  • Workshop "Effective theories in classical and quantum particle systems", SwissMAP Research Station, Les Diablerets, Switzerland (June 18-23, 2023)
  • Seminar, University of Warsaw (May 25, 2023)
  • Talk in the seminar "Mathematics of Many-Body Systems", SISSA Trieste (March 9, 2023)
  • Mini-Workshop on fermionic quantum systems, Center for Advanced Studies LMU (CAS) - LMU München, Munich, Germany (January 23-24, 2023).
  • Oberseminar Analysis, Hausdorff Center for Mathematics/University of Bonn (January 12, 2023)
  • Workshop Mathematical Quantum Matter, University of Milan (January 9 - 11, 2023)
  • ICMP 2021, Geneva (2-7 August 2021)

Bosonization of Fermionic Many-Body Dynamics.

Effective Theories in Many-Body Quantum Mechanics: an introduction and overview of recent developments.

Correlation energy of a weakly interacting Fermi gas, as obtained by bosonizing collective particle-hole pair excitations. This provides the corresponding lower bound to the results presented below, in accordance with the random phase approximation.

  • Conference "Mathematical results of many-body quantum systems", Herrsching near Munich (June 6-11, 2022).
  • On-Line QLunch, University of Copenhagen (29 April 2020)

We calculate the correlation energy of the mean-field Fermi gas by bosonizing collective particle-hole pair excitations; this makes the random phase approximation rigorous as an upper bound.

  • "CPS-Workshop", University of Mannheim (January 2020)
  • Mathematical Physics Seminar, LMU Munich (November 2019)
  • Conference "Dynamics, Equations and Applications" (DEA 2019), Kraków (September 2019)
  • Conference "QMath 14: Mathematical Results in Quantum Physics", Aarhus University (August 2019)
  • Conference "On Mathematical Aspects of Interacting Particle Systems in Low Dimension", FernUniversität Hagen (June 2019)
  • Mathematical Physics Seminar, University of Vienna (June 2019)
  • Workshop "Mean-Field and other Effective Models in Mathematical Physics", Fondation Les Treilles (May 2019)
  • Workshop "Many-body theory, effective equations and PDEs", Mittag-Leffler Institute, The Royal Swedish Academy of Sciences, Stockholm (March 2019)
  • Seminar at Gran Sasso Science Institute, L'Aquila (7 March 2019)
  • Seminar at Università degli Studi Roma Tre (27 November 2018)
  • Quantum Lunch, University of Copenhagen, one hour seminar talk (7 November 2018)
  • ICMP 2018 Montreal, contributed talk (July 2018)

Reformulation of the Dirac-Frenkel principle in terms of reduced density matrices and application to the derivation of Hartree-Fock and Bogoliubov-de-Gennes equations:

Interaction corrections to spin-wave theory of the ferromagnetic quantum Heisenberg model, and perturbative analysis of spin-waves at low temperature:

Derivation of the time-dependent Hartree-Fock equation for pure and mixed fermionic states in the mean-regime, and derivation of the Vlasov equation:

Quantitative Derivation of the Gross-Pitaevskii equation:

Slides of my PhD defence:

Anderson localization at large disorder on a lattice (method of fractional moments):

Fermionic coherent states with and without Grassmann numbers:

Dynamics of the radiative decay of excited atoms, rate of relaxation:

Existence of asymptotic fields in non-relativistic quantum electrodynamics: