The Ground State Energy Is Not Always Convex in the Number of Electrons
speaker: Simone Di Marino (Università di Genova )abstract: We provide the first counter-example showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This property had been conjectured to hold for decades and it plays an important role in quantum chemistry. Our counter-example involves an external potential generated by six nuclei of small fractional charges, placed far away from each other. This is an application of Gran Canonical Optimal Transport which is the convex relaxation of multimarginal optimal transport, and it can be seen as the dual to a kinetic-less ground state energy with respect to the external potential. The lack of convexity of the ground state energy is then equivalent to the lack of convexity of Canonical (multimarginal) optimal transport which can be proven to hold for a discrete measure with six atoms.
timetable:
Wed 4 Dec, 9:50 - 10:35, Aula Dini
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