# Universal Low-energy Behavior in a Quantum Lorentz Gas with Gross-Pitaevskii Potentials

@article{Basti2018UniversalLB, title={Universal Low-energy Behavior in a Quantum Lorentz Gas with Gross-Pitaevskii Potentials}, author={Giulia Basti and Serena Cenatiempo and Alessandro Teta}, journal={Mathematical Physics, Analysis and Geometry}, year={2018}, volume={21}, pages={1-25} }

We consider a quantum particle interacting with N obstacles, whose positions are independently chosen according to a given probability density, through a two-body potential of the form N2V (Nx) (Gross-Pitaevskii potential). We show convergence of the N dependent one-particle Hamiltonian to a limiting Hamiltonian where the quantum particle experiences an effective potential depending only on the scattering length of the unscaled potential and the density of the obstacles. In this sense our… CONTINUE READING

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