A Phenomenological Operator Description of Dynamics of Crowds: Escape Strategies

We adopt an operatorial method, based on creation, annihilation and number operators, to describe one or two populations mutually interacting and moving in a two–dimensional region. In particular, we discuss how the two populations, contained in a certain two-dimensional region with a non–trivial topology, react when some alarm occurs. We consider the cases of both low and high densities of the populations, and discuss what is changing as the strength of the interaction increases. We also analyze what happens when the region has either a single exit or two ways out.