7 citations · 19 across the 7 of their papers we have counts for
7 papers
Transport and generation of macroscopically modulated waves in diatomic chains
Johannes Giannoulis
We derive and justify analytically the dynamics of a small macroscopically modulated amplitude of a single plane wave in a nonlinear diatomic chain with stabilizing on-site potenti…
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Luigi Ambrosio, Alessio Figalli, Gero Friesecke +2
In this paper we study the semiclassical limit of the Schrödinger equation. Under mild regularity assumptions on the potential which include Born-Oppenheimer potential energy s…
High-frequency averaging in semi-classical Hartree-type equations
Johannes Giannoulis, Alexander Mielke, Christof Sparber
We investigate the asymptotic behavior of solutions to semi-classical Schroedinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validi…
Passage from quantum to classical molecular dynamics in the presence of Coulomb interactions
Luigi Ambrosio, Gero Friesecke, Jannis Giannoulis
We present a rigorous derivation of classical molecular dynamics (MD) from quantum molecular dynamics (QMD) that applies to the standard Hamiltonians of molecular physics with Coul…
Interaction of modulated pulses in scalar multidimensional nonlinear lattices
Johannes Giannoulis
We investigate the macroscopic dynamics of sets of an arbitrary finite number of weakly amplitude-modulated pulses in a multidimensional lattice of particles. The latter are assume…
Lagrangian and Hamiltonian two-scale reduction
Johannes Giannoulis, Michael Herrmann, Alexander Mielke
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dy…