The Hartree functional in a double well

Abstract

We consider a non-linear Hartree energy for bosonic particles in a symmetric double-well potential. In the limit where the wells are fare apart and the potential barrier is high, we prove that the ground state and first excited state are given to leading order by an even, respectively odd, superposition of ground states in single wells. We evaluate the resulting tunneling term splitting the corresponding energies precisely.

The results are inputs in a forthcoming joint work with Dominique Spehner