Precise intermittency for the parabolic Anderson equation with an (1+1)-dimensional time-space white noise

The moment Lyapunov exponent is computed for the solution of the parabolic Anderson equation with an (1 + 1)-dimensional time-space white noise. Our main result positively confirms an open problem posted in (Ann. Probab. (2015) to appear) and originated from the observations made in the physical literature (J. Statist. Phys. 78 (1995) 1377-1401) and (Nuclear Physics B 290 (1987) 582-602). By a link through the Feynman-Kac's formula, our theorem leads to the evaluation of the ground state energy for the n-body problem with Dirac pair interaction.