Niels Benedikter

Upcoming Talks
  • Conference on Quantum Statistical Mechanics, Toulouse Mathematics Institute, 27-31 May 2024
  • One World IAMP Mathematical Physics Seminar, online, 4 June 2024
  • XXI International Congress On Mathematical Physics, Strasbourg, contributed talk, 1-6 July 2024
  • European Congress of Mathematics, Mini-Symposium "Collective Phenomena of Fermionic Systems", Seville, 15-19 July 2024
  • Mathematical Challenges in Quantum Mechanics, school and workshop, GSSI L'Aquila, 10-14 February 2025
  • Emergent phenomena in many-body quantum systems, CIRM, 8-12 December 2025
Past Scientific Talks

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:

Undergraduate Studies: Seminar Talks

In a 2+1 dimensional nonlinear Sigma model with Hopf term there exist topological excitations (skyrmions), which can have arbitrary spin (not necessarily integer or half-integer) and arbitrary quantum statistics (arbitrary phases under permutation of particles). Skyrmions have be found in experiments, see e.g. X. Z. Yu et al.
A short theoretical introduction to this interesting topic can be found in the book "Quantum Field Theory" by Kerson Huang (Wiley 1998) in the chapter on topological excitations.

Physics talks (in German) at the "Naturwissenschaftliches Kolleg" of the Studienstiftung (German National Academic Foundation).

  • Quantitative Derivation of the Gross-Pitaevskii Equation (November 2012)
  • Exact Renormalisation Group and Asymptotic Safety of Gravity (November 2011)
  • Homotopie-Gruppen für Physiker, Anyonen in 2+1 Dimensionen (Oktober 2010)
  • Konforme Feldtheorie (April 2010)
  • Majorana-Spinoren (September 2008)
  • Farbladungsspiel (September 2008)
  • Das Wu-Experiment (April 2008)