  In this work, we study the quantum fluctuation dynamics in a Bose gas on a
torus $\Lambda=(L\mathbb{T})^3$ that exhibits Bose-Einstein condensation,
beyond the leading order Hartree-Fock-Bogoliubov (HFB) fluctuations. Given a
Bose-Einstein condensate (BEC) with density $N$ surrounded by thermal
fluctuations with density $1$, we assume that the system is described by a
mean-field Hamiltonian. We extract a quantum Boltzmann type dynamics from a
second-order Duhamel expansion upon subtracting both the BEC dynamics and the
HFB dynamics. Using a Fock-space approach, we provide explicit error bounds. It
is known that the BEC and the HFB fluctuations both evolve at microscopic time
scales $t\sim1$. Given a quasifree initial state, we determine the time
evolution of the centered correlation functions $\langle a\rangle$, $\langle
aa\rangle-\langle a\rangle^2$, $\langle a^+a\rangle-|\langle a\rangle|^2$ at
mesoscopic time scales $t\sim\lambda^{-2}$, where $0<\lambda\ll1$ denotes the
size of the HFB interaction. For large but finite $N$, we consider both the
case of fixed system size $L\sim1$, and the case $L\sim \lambda^{-2-}$. In the
case $L\sim1$, we show that the Boltzmann collision operator contains
subleading terms that can become dominant, depending on time-dependent
coefficients assuming particular values in $\mathbb{Q}$; this phenomenon is
reminiscent of the Talbot effect. For the case $L\sim \lambda^{-2-}$, we prove
that the collision operator is well approximated by the expression predicted in
the literature. In either of those cases, we have $\lambda\sim \Big(\frac{\log
\log N}{\log N}\Big)^{\alpha}$, for different values of $\alpha>0$.
