97 citations · 446 across the 19 of their papers we have counts for
23 papers
Particle-Hole Pair Localization on the Fermi Surface and its Impact on the Correlation Energy
Niels Benedikter
In recent years it has been shown how approximate bosonization can be used to justify the random phase approximation for the correlation energy of interacting fermions in a mean-fi…
Mesoscopic Observables of the Dilute Fermi Gas at Low Energy
Niels Benedikter, Emanuela L. Giacomelli, Asbjørn Bækgaard Lauritsen +1
We consider a dilute quantum gas of interacting spin-1/2 fermions in the thermodynamic limit. For a trial state that resolves the ground state energy to the precision of the Huang-…
Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation
Niels Benedikter, Sascha Lill, Diwakar Naidu
We analyse the momentum distribution of a three-dimensional Fermi gas in the mean-field scaling regime in a trial state that was recently proven to reproduce the Gell-Mann-Brueckne…
Derivation of Hartree-Fock Dynamics and Semiclassical Commutator Estimates for Fermions in a Magnetic Field
Niels Benedikter, Chiara Boccato, Domenico Monaco +1
We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show th…
Momentum Distribution of a Fermi Gas in the Random Phase Approximation
Niels Benedikter, Sascha Lill
We consider a system of interacting fermions on the three-dimensional torus in a mean-field scaling limit. Our objective is computing the occupation number of the Fourier modes in…
Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation
Niels Benedikter, Davide Desio
We revisit the derivation of the time-dependent Hartree-Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comme…
Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation
Niels Benedikter
I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective…
Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
Niels Benedikter, Marcello Porta, Benjamin Schlein +1
Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interactio…
Bosonization of Fermionic Many-Body Dynamics
Niels Benedikter, Phan Thành Nam, Marcello Porta +2
We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial d…
Correlation Energy of a Weakly Interacting Fermi Gas
Niels Benedikter, Phan Thành Nam, Marcello Porta +2
We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the…
Bosonic Collective Excitations in Fermi Gases
Niels Benedikter
Hartree-Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessar…
Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
Niels Benedikter, Phan Thành Nam, Marcello Porta +2
While Hartree-Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correl…
The Dirac-Frenkel Principle for Reduced Density Matrices, and the Bogoliubov-de-Gennes Equations
Niels Benedikter, Jérémy Sok, Jan Philip Solovej
The derivation of effective evolution equations is central to the study of non-stationary quantum many-body sytems, and widely used in contexts such as superconductivity, nuclear p…
Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals
Dorothea Golze, Niels Benedikter, Marcella Iannuzzi +2
An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local o…
Interaction Corrections to Spin-Wave Theory in the Large-S Limit of the Quantum Heisenberg Ferromagnet
Niels Benedikter
The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculat…
Effective Evolution Equations from Quantum Dynamics
Niels Benedikter, Marcello Porta, Benjamin Schlein
In these notes we review the material presented at the summer school on "Mathematical Physics, Analysis and Stochastics" held at the University of Heidelberg in July 2014. We consi…
From the Hartree dynamics to the Vlasov equation
Niels Benedikter, Marcello Porta, Chiara Saffirio +1
We consider the evolution of quasi-free states describing fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large , we study t…
Mean-field Evolution of Fermionic Mixed States
Niels Benedikter, Vojkan Jaksic, Marcello Porta +2
In this paper we study the dynamics of fermionic mixed states in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitab…
Hartree-Fock dynamics for weakly interacting fermions
Niels Benedikter, Marcello Porta, Benjamin Schlein
We review recent results concerning the evolution of fermionic systems. We are interested in the mean field regime, where particles experience many weak collisions. For fermions, t…
Deriving the Gross-Pitaevskii equation
Niels Benedikter
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evoluti…
Mean-Field Dynamics of Fermions with Relativistic Dispersion
Niels Benedikter, Marcello Porta, Benjamin Schlein
We extend the derivation of the time-dependent Hartree-Fock equation recently obtained in [2] to fermions with a relativistic dispersion law. The main new ingredient is the propaga…
Mean-field Evolution of Fermionic Systems
Niels Benedikter, Marcello Porta, Benjamin Schlein
The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared wit…
Quantitative Derivation of the Gross-Pitaevskii Equation
Niels Benedikter, Gustavo de Oliveira, Benjamin Schlein
Starting from first principle many-body quantum dynamics, we show that the dynamics of Bose-Einstein condensates can be approximated by the time-dependent nonlinear Gross-Pitaevski…