Below you find a list of my publications with links to the arxiv versions. Please consult my research overview (as PDF) for short explanations of my results.
Correlation Energy of the Fermi Gas
We derive a formula of the type proposed by Gell-Mann and Brueckner as an upper bound for the correlation energy of the Fermi gas in the mean-field scaling regime.
- N. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer: Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime, arXiv:1809.01902 [math-ph]
Spin Wave Theory
We study corrections to the free energy in the Quantum Heisenberg Ferromagnet due to remainder interaction effects in the Spin Wave Theory.
- N. Benedikter: Interaction Corrections to Spin-Wave Theory in the in the Large-S Limit of the Quantum Heisenberg Ferromagnet, Mathematical Physics, Analysis, and Geometry 20, 1-21 (2017)
Efficient Evaluation of Solid Harmonic Gaussian Integrals
We derive explicit formulas for certain integrals in numerical quantum chemistry calculations.
- D. Golze, N. Benedikter, M. Iannuzzi, J. Wilhelm, and J. Hutter: Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals, Journal of Chemical Physics 146, 034105 (2017)
Effective Evolution Equations
We derive the fermionic Bogoliubov-de-Gennes equations (Hartree-Fock equations with pairing density) and the bosonic Hartree-Fock-Bogoliubov equations from a reformulation of the geometric Dirac-Frenkel principle, proving optimality of these approximations. We also give a proof of well-posedness for the Bogoliubov-de-Gennes equations.
- N. Benedikter, J. Sok, and J.P. Solovej: The Dirac-Frenkel Principle for Reduced Density Matrices, and the Bogoliubov-de-Gennes Equations, Annales Henri Poincaré, 19(4), 1167-1214 (2018)
In the following lecture notes we discuss a wide range of results concerning effective evolution equations for bosonic and fermionic systems.
- N. Benedikter, M. Porta, and B. Schlein: Effective Evolution Equations from Quantum Dynamics (2016), in SpringerBriefs in Mathematical Physics
The many-body Schrödinger equation in certain scaling regimes gives rise to effective nonlinear dynamics. An overview can be found in my thesis:
- N. Benedikter: Effective Evolution Equations from Many-Body Quantum Mechanics, (2014) Thesis University of Bonn
Fermionic Effective Evolution Equations
We derive the Hartree-Fock equation as governing the effective dynamics of fermions in the mean-field regime. In a recent paper, we extend the derivation to mixed states as initial data. As a second step of approximation, we derive the Vlasov equation.
- N. Benedikter, M. Porta. C. Saffirio, and B. Schlein: From the Hartree dynamics to the Vlasov equation, ARMA 221, 273-334 (2016)
- N. Benedikter, V. Jaksic, M. Porta, C. Saffirio, and B. Schlein: Mean-field Evolution of Fermionic Mixed States, Comm. Pure Appl. Math. 69, 2250-2303 (2014)
- N. Benedikter, M. Porta, and B. Schlein: Hartree-Fock dynamics for weakly interacting fermions (2014), in Proceedings of the QMath12 Conference
- N. Benedikter, M. Porta, and B. Schlein: Mean-Field Dynamics of Fermions with Relativistic Dispersion, J. Math. Phys. 55, 021901 (2014)
- N. Benedikter, M. Porta, and B. Schlein: Mean-field Evolution of Fermionic Systems, Comm. Math. Phys. 331, 1087-1131 (2014)
Bosonic Effective Evolution Equation
We derive the Gross-Pitaevskii equation describing the dynamics of dilute Bose-Einstein condensates:
- N. Benedikter: Deriving the Gross-Pitaevskii Equation (2014), in Proceedings of the QMath12 Conference
- N. Benedikter, G. de Oliveira, and B. Schlein: Quantitative Derivation of the Gross-Pitaevskii Equation, Comm. Pure Appl. Math. 68, 1399-1482 (2014)
Physical experience shows that excited atoms relax to the ground state by emission of photons. We study the rate of relaxation in models of non-relativistic quantum electrodynamics:
- N. Benedikter: Dynamics of the Radiative Decay of Excited Atoms (2010), Diploma thesis at the University of Stuttgart