34 citations · 148 across the 18 of their papers we have counts for
18 papers
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…
Norm approximation for the Fröhlich dynamics in the mean-field regime
Nikolai Leopold
We study the time evolution of the Fröhlich Hamiltonian in a mean-field limit in which many particles weakly couple to the quantized phonon field. Assuming that the particles are i…
Derivation of the Maxwell-Schrödinger Equations: A note on the infrared sector of the radiation field
Marco Falconi, Nikolai Leopold
We slightly extend prior results about the derivation of the Maxwell-Schrödinger equations from the bosonic Pauli-Fierz Hamiltonian. More concretely, we show that the findings from…
Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
Nikolai Leopold, Chiara Saffirio
We investigate the semiclassical limit from the semi-relativistic Hartree-Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relati…
Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
Marco Falconi, Nikolai Leopold, David Mitrouskas +1
We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quant…
Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
Nikolai Leopold, David Mitrouskas, Simone Rademacher +2
We consider the Fröhlich Hamiltonian with large coupling constant . For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corres…
Derivation of the Landau-Pekar equations in a many-body mean-field limit
Nikolai Leopold, David Mitrouskas, Robert Seiringer
We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle number and suitably small co…
The Landau-Pekar equations: Adiabatic theorem and accuracy
Nikolai Leopold, Simone Rademacher, Benjamin Schlein +1
We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution genera…
Theory of the Rotating Polaron: Spectrum and Self-Localization
Enderalp Yakaboylu, Bikashkali Midya, Andreas Deuchert +2
We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a `rotating polar…
Mean-field Dynamics for the Nelson Model with Fermions
Nikolai Leopold, Sören Petrat
We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take…
Mean-field limits of particles in interaction with quantized radiation fields
Nikolai Leopold, Peter Pickl
We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Ex…
Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
Nikolai Leopold, Peter Pickl
We consider the spinless Pauli-Fierz Hamiltonian which describes a quantum system of non-relativistic identical particles coupled to the quantized electromagnetic field. We study t…
Derivation of the Time Dependent Gross-Pitaevskii Equation in Two Dimensions
Maximilian Jeblick, Nikolai Leopold, Peter Pickl
We present a microscopic derivation of the defocusing two-dimensional cubic nonlinear Schrödinger equation as a mean field equation starting from an interacting -particle system…