4 papers
Towards the quantum Brownian motion
Laszlo Erdos, Manfred Salmhofer, Horng-Tzer Yau
We consider random Schrödinger equations on $\bR^d$ or $\bZ^d$ for with uncorrelated, identically distributed random potential. Denote by the coupling constant and $ψ_…
Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons
Alexander Elgart, Laszlo Erdos, Benjamin Schlein +1
We consider the dynamics of boson systems interacting through a pair potential where . We denote the solution to the -particl…
Derivation of the Gross-Pitaevskii Hierarchy for the Dynamics of Bose-Einstein Condensate
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
Consider a system of bosons on the three dimensional unit torus interacting via a pair potential , where $\bx=(x_1, ..., x_N)$ denotes the positions of the pa…
Nonlinear Hartree equation as the mean field limit of weakly coupled fermions
Alexander Elgart, Laszlo Erdos, Benjamin Schlein +1
We consider a system of N weakly interacting fermions with a real analytic pair interaction. We prove that for a general class of initial data there exists a fixed time T such that…