Benjamin Schlein

Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems

We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.

Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices

We consider

Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential

N\times N

Rigorous Derivation of the Gross-Pitaevskii Equation

Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order

Quantitative Derivation of the Gross-Pitaevskii Equation

1/N

Rate of Convergence Towards Hartree Dynamics

. We study the connection between eigenvalue statistics on microscopic energy scales

Dynamical Collapse of Boson Stars

\eta\ll1

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

and (de)localization properties of the eigenvectors. Under suitable assumptions on the distribution of the single matrix elements, we first give an upper bound on the density of states on short energy scales of order

Quantum Dynamics with Mean Field Interactions: a New Approach

\eta \sim\log N/N

Ground-state energy of a low-density Bose gas: A second-order upper bound

. We then prove that the density of states concentrates around the Wigner semicircle law on energy scales