10 papers · 1 filter
Derivation of the Maxwell-Schrödinger and Vlasov-Maxwell Equations from Non-Relativistic QED
Nikolai Leopold
We study the spinless Pauli-Fierz Hamiltonian in a semiclassical mean-field limit of many fermions. For appropriate initial conditions, we prove, in the trace norm topology of redu…
Ground state of Bose gases interacting through singular potentials
Lea Boßmann, Nikolai Leopold, Sören Petrat +1
We consider a system of bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form for .…
Derivation of the Vlasov-Maxwell system from the Maxwell-Schrödinger equations with extended charges
Nikolai Leopold, Chiara Saffirio
We consider the Maxwell-Schrödinger equations in the Coulomb gauge describing the interaction of extended fermions with their self-generated electromagnetic field. They heuristical…
A Note on the Binding Energy for Bosons in the Mean-field Limit
Lea Boßmann, Nikolai Leopold, David Mitrouskas +1
We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose-Einstein condensation. The binding energy is defined as the energy it takes to remove…
Renormalized Bogoliubov Theory for the Nelson Model
Marco Falconi, Jonas Lampart, Nikolai Leopold +1
We consider the time evolution of the renormalized Nelson model, which describes bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles…
Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications
Lea Boßmann, Nikolai Leopold, David Mitrouskas +1
We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two appli…