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).
© 2015 AIP Publishing LLC. Received 17 December 2014; accepted 3 February 2015; published online 18 February 2015. The authors are grateful to Jan Philip Solovej for useful discussions about Theorem 1.1. Work is partially supported by Fondecyt (Chile) project 112–0836 and the Iniciativa Científica Milenio (Chile) through the Millenium Nucleus RC–120002 "Física Matemática" (R.D.B.), and NSF Grant Nos. PHY–1347399 and DMS–1363432 (R.L.F.); PHY–0965859 and PHY–1265118 (E.H.L.)
Published - 1.4908125.pdf
Submitted - 1409.5415v1.pdf