We investigate the dynamics of a boson gas with three-body interactions in dimensions d = 1, 2. We prove that in the limit where the particle number N tends to infinity, the BBGKY hierarchy of… (More)

for the validity of this result. Furthermore, we derive the macroscopic limit of the quantum dynamics in this system, and prove that it is governed by the linear Boltzmann equations. The present… (More)

We consider the dynamical Gross-Pitaevskii (GP) hierarchy on Rd, d ≥ 1, for cubic, quintic, focusing and defocusing interactions. For both the focusing and defocusing case, and any d ≥ 1, we prove… (More)

We derive the defocusing cubic Gross-Pitaevskii (GP) hierarchy in dimensions d = 2, 3, from an N -body Schrödinger equation describing a gas of interacting bosons in the GP scaling, in the limit N →… (More)

We study the macroscopic scaling and weak coupling limit for a random Schrödinger equation on Z. We prove that the Wigner transforms of a large class of ”macroscopic” solutions converge in r-th mean… (More)

Abstract. We study a class of Schrödinger operators on Z with a random potential decaying as |x|, 0 < σ ≤ 1 2 , in the limit of small disorder strength λ. For the critical exponent σ = 1 2 , we prove… (More)

Abstract. We prove lower bounds on the localization length of eigenfunctions in the threedimensional Anderson model at weak disorders. Our results are analogous to those obtained by Shubin, Schlag… (More)

We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction… (More)

We construct infraparticle scattering states for Compton scattering in the standard model of non-relativistic QED. In our construction, an infrared cutoff initially introduced to regularize the model… (More)

We consider the quantum mechanical dynamics of an electron against a background lattice of impurity ions exhibiting randomly distributed interaction strengths. Models of this type (Anderson model)… (More)