  We discuss the amplification of loop corrections in quantum many-body systems
through dynamical instabilities. As an example, we investigate both
analytically and numerically a two-component ultracold atom system in one
spatial dimension. The model features a tachyonic instability, which
incorporates characteristic aspects of the mechanisms for particle production
in early-universe inflaton models. We establish a direct correspondence between
measureable macroscopic growth rates for occupation numbers of the ultracold
Bose gas and the underlying microscopic processes in terms of Feynman loop
diagrams. We analyze several existing ultracold atom setups featuring dynamical
instabilities and propose optimized protocols for their experimental
realization. We demonstrate that relevant dynamical processes can be enhanced
using a seeding procedure for unstable modes and clarify the role of initial
quantum fluctuations and the generation of a non-linear secondary stage for the
amplification of modes.
