Dynamical systems having a generic graph as ambient space are described by mean of a discrete differential calculus. A symplectic structure is naturally introduced and it is found that functions defined over the vertices of the graph are canonically conjugated to functions defined over the edges. Heisenberg-like inequalities and Schrodinger-like equations of motion are then obtained without need of a true quantization of the dynamics.

Reference: Battaglia D., Rasetti M., "Quantum-like diffusions over discrete sets", Physics Letters A (2003), in press.