Quantum physics and complex networks

There is a widely used and successful theory of ``chemical reaction networks,'' which provides a framework describing systems governed by mass action kinetics. Computer science and population biology use the same ideas under a different name: ``stochastic Petri nets.'' But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas---yet in a context where probabilities replace amplitudes. I will explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics which we've produced several results on recently [1, 2, 3], including the recent analytical results uniting quantum physics and complex networks [2]. Our general idea is about merging concepts from quantum physics and complex network theory [1, 2, 3, 4] to provide a bidirectional bridge between both disciplines.\\[4pt] [1] Quantum Techniques for Stochastic Mechanics, 235 pages, arXiv:1209.3632 (2012);\\[0pt] [2] Degree Distribution in Quantum Walks on Complex Networks, Phys. Rev. X 3, 041007 (2013);\\[0pt] [3] Quantum Transport Enhancement by Time-Reversal Symmetry Breaking, Sci. Rep. 3, 2361 (2013);\\[0pt] [4] Community Detection in Quantum Complex Networks, arXiv:1310.6638 (2013).