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5 papers · 2 filters
Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics
Igor Rodnianski, Benjamin Schlein
The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of…
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
Rafael D. Benguria, Rupert L. Frank, Michael Loss
It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality…
On the ground state energy of the translation invariant Pauli-Fierz model
Jean-Marie Barbaroux, Thomas Chen, Vitali Vougalter +1
In this note, we determine the ground state energy of the translation invariant Pauli-Fierz model to subleading order with respect to powers of the finestructure constant…
The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction
Rupert L. Frank, Heinz Siedentop, Simone Warzel
We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction…
On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
Sergiu Klainerman, Matei Machedon
We give a new proof of uniqueness of solutions to the Gross-Pitaevskii hierarchy, first established by Erdos, Schlein and Yau, in a different space, based on space-time estimates.