  We present a method for computing the non-perturbative mass-gap in the theory
of Bosonic membranes in flat background spacetimes with or without background
fluxes. The computation of mass-gaps is carried out using a matrix
regularization of the membrane Hamiltonians. The mass gap is shown to be
naturally organized as an expansion in a 'hidden' parameter, which turns out to
be $\frac{1}{d}$: d being the related to the dimensionality of the background
space. We then proceed to develop a large $N$ perturbation theory for the
membrane/matrix-model Hamiltonians around the quantum/mass corrected effective
potential. The same parameter that controls the perturbation theory for the
mass gap is also shown to control the Hamiltonian perturbation theory around
the effective potential. The large $N$ perturbation theory is then translated
into the language of quantum spin chains and the one loop spectra of various
Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop
effective Hamiltonians for membranes in flat space times. Apart from membranes
in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for
non-critical membranes in plane wave type spacetimes are also analyzed within
the paradigm of quantum spin chains and the Bosonic sectors of all the models
proposed in (hep-th/0607005) are diagonalized at the one-loop level.
