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math-ph2024★ 8 cited
Ground state energy is not always convex in the number of electrons
Simone Di Marino, Mathieu Lewin, Luca Nenna
We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. T…
math.AP2024
A variational formulation of a Multi-Population Mean Field Games with non-local interactions
Luigi De Pascale, Luca Nenna
We propose a MFG model with quadratic Hamiltonian involving populations. This results in a system of Hamilton-Jacobi-Bellman and Fokker-Planck equations with non-local…
math.OC2024
An ordinary differential equation for entropic optimal transport and its linearly constrained variants
Joshua Zoen-Git Hiew, Luca Nenna, Brendan Pass
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete margina…