  Nonlinearities in the dispersion relations associated with different
interactions designs, boundary conditions and the existence of a physical
cut-off scale can alter the quantum vacuum energy of a nonrelativistic system
nontrivially. As a material realization of this, we consider a 1D-periodic
rotating, interacting non-relativistic setup. The quantum vacuum energy of such
a system is expected to comprise two contributions: a fluctuation-induced
quantum contribution and a repulsive centrifugal-like term. We analyze the
problem in detail within a complex Schoedinger quantum field theory with a
quartic interaction potential and perform the calculations non-perturbatively
in the interaction strength by exploiting the nonlinear structure of the
associated nonlinear Schroedinger equation. Calculations are done in both
zeta-regularization, as well as by introducing a cut-off scale. We find a
generic, regularization-independent behavior, where the competition between the
interaction and rotation can be balanced at some critical ring-size, where the
quantum vacuum energy has a maxima and the force changes sign. The inclusion of
a cut-off smoothes out the vacuum energy at small distance but leaves unaltered
the long distance behavior. We discuss how this behavior can be tested with
ultracold-atoms.
