TY - JOUR AB - We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory. AU - Nam, Phan AU - Napiórkowski, Marcin M ID - 484 IS - 3 JF - Advances in Theoretical and Mathematical Physics SN - 10950761 TI - Bogoliubov correction to the mean-field dynamics of interacting bosons VL - 21 ER - TY - JOUR AB - We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices. AU - Bourgade, Paul AU - Erdös, László AU - Yau, Horng AU - Yin, Jun ID - 483 IS - 3 JF - Advances in Theoretical and Mathematical Physics SN - 10950761 TI - Universality for a class of random band matrices VL - 21 ER -