112 citations · 725 across the 43 of their papers we have counts for
21 papers · 1 filter
Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit
Gheorghe Nenciu, Evelyn Richman, Christof Sparber
We study the large field limit in Schrödinger equations with magnetic vector potentials describing translationally invariant -fields with respect to the -axis. In a first ste…
Averaging of nonlinear Schrödinger equations with strong magnetic confinement
Rupert L. Frank, Florian Méhats, Christof Sparber
We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement,…
Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures
Jack Arbunich, Christof Sparber
We consider a nonlinear Schroedinger equation in two spatial dimensions subject to a periodic honeycomb lattice potential. Using a multi-scale expansion together with rigorous erro…
Weakly nonlinear time-adiabatic theory
Christof Sparber
We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schroedinger equations in which eit…
Ground state properties of graphene in Hartree-Fock theory
Christian Hainzl, Mathieu Lewin, Christof Sparber
We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we re…
WKB analysis of Bohmian dynamics
A. Figalli, C. Klein, P. Markowich +1
We consider a semi-classically scaled Schrödinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in m…
Nonlinear dynamics of semiclassical coherent states in periodic potentials
Rémi Carles, Christof Sparber
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experimen…
Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials
Rémi Carles, Christof Sparber
We consider semiclassically scaled Schrodinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of se…
On the dynamics of Bohmian measures
Peter Markowich, Thierry Paul, Christof Sparber
The present work is devoted to the study of dynamical features of Bohmian measures, recently introduced by the authors. We rigorously prove that for sufficiently smooth wave functi…
Bohmian measures and their classical limit
Peter Markowich, Thierry Paul, Christof Sparber
We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics (when written in a Lagrangian form). We study the so-called cl…
Classical limit for semi-relativistic Hartree systems
Gonca L. Aki, Peter A. Markowich, Christof Sparber
We consider the three-dimensional semi-relativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the init…
On the Gross-Pitaevskii equation for trapped dipolar quantum gases
Rémi Carles, Peter Markowich, Christof Sparber
We study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-…
Geometric currents in piezoelectricity
Gianluca Panati, Christof Sparber, Stefan Teufel
As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adi…
Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
C. Klein, P. Markowich, C. Sparber
The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analy…
Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation
Christian Hainzl, Mathieu Lewin, Christof Sparber
We consider a generalized Dirac-Fock type evolution equation deduced from no-photon Quantum Electrodynamics, which describes the self-consistent time-evolution of relativistic elec…
Effective mass theorems for nonlinear Schroedinger equations
Christof Sparber
We consider time-dependent nonlinear Schroedinger equations subject to smooth, lattice-periodic potentials plus additional confining potentials, slowly varying on the lattice scale…
Semiclassical asymptotics for weakly nonlinear Bloch waves
Remi Carles, Peter A. Markowich, Christof Sparber
We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schroedinger equations with a fast periodic potential and a slowly varying conf…
Quantum dynamical semigroups for diffusion models with Hartree interaction
Anton Arnold, Christof Sparber
We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this clas…
Semiclassical Asymptotics for the Maxwell - Dirac System
C. Sparber, P. Markowich
We study the coupled system of Maxwell and Dirac equations from a semiclassical point of view. A rigorous nonlinear WKB-analysis, locally in time, for solutions of (critical) order…
On the Long Time Behavior of the Quantum Fokker-Planck equation
C. Sparber, J. A. Carrillo, J. Dolbeault +1
We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of…
Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics
Christof Sparber, Peter A. Markowich, Norbert J. Mauser
We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is…