Ground state energy of large polaron systems
  The last unsolved problem about the many-polaron system, in the Pekar-Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the 'neutral case'). We prove that the ground state energy, for large $N$, goes exactly as $-N^{7/5}$, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of $2^{2/5}$. 
Rafael D. Benguria, Rupert L. Frank, Elliott H. Lieb
math-ph math.AP math.MP