  We introduce simple generic models of surface dynamics in loop quantum
gravity (LQG). A quantum surface is defined as a set of elementary patches of
area glued together. We provide it with an extra structure of locality (nearest
neighbors), thought of as induced by the whole spin network state defining the
3d bulk geometry around the quantum surface. Here, we focus on classical
surface dynamics, using a spinorial description of surface degrees of freedom.
We introduce two classes of dynamics, to be thought as templates for future
investigation of LQG dynamics with in mind the dynamics of quantum black holes.
The first defines global dynamics of the closure defect of the surface, with
two basic toy-models, either a dissipative dynamics relaxing towards the
closure constraint or a Hamiltonian dynamics precessing the closure defect. The
second class of dynamics describes the isolated regime, when both area and
closure defect are conserved throughout the evolution. The surface dynamics is
implemented through U(N) transformations and generalizes to a Bose-Hubbard
Hamiltonian with a local quadratic potential interaction. We briefly discuss
the implications of modeling the quantum black hole dynamics by a surface
Bose-Hubbard model.
