14 citations · 14 across the 1 of their papers we have counts for
4 papers
The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states
David Gontier, Mathieu Lewin, Faizan Q. Nazar
We study the nonlinear Schrödinger equation for systems of orthonormal functions. We prove the existence of ground states for all when the exponent of the non linearity…
Geometry Equilibration of Crystalline Defects in Quantum and Atomistic Descriptions
Huajie Chen, Faizan Q. Nazar, Christoph Ortner
We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a di…
Convergence Rates from Yukawa to Coulomb Interaction in the Thomas-Fermi-von Weizsäcker Model
Faizan Q. Nazar
We establish uniform convergence, with explicit rate, of the solution to the Thomas--Fermi--von Weizsäcker (TFW) Yukawa model to the solution of the TFW Coulomb model, for general…
Locality of the Thomas-Fermi-von Weizsäcker Equations
Faizan Q. Nazar, Christoph Ortner
We establish a pointwise stability estimate for the Thomas-Fermi-von Weizsäcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a…