Speaker
Description
Many real-world complex systems — from biochemical networks and ecological dynamics to epidemics and socioeconomic models — share a common mathematical structure: agents or particles that move, interact, and change in number. Stochastic reaction-diffusion processes provide a natural and unifying framework to model this broad class of systems, yet their standard probabilistic formulations become unwieldy due to combinatorial complexity arising from nonlinear interactions and varying particle numbers. In this talk, I will show how quantum-inspired methods — second quantization, Fock space, creation and annihilation operators, and path integrals — offer an elegant and powerful alternative. Originally developed for quantum field theory, these tools can be brought into the classical domain of stochastic systems, where they handle combinatorial bookkeeping automatically and enable systematic derivations of emergent behavior at multiple scales. I will present a unifying field theory representation that encompasses previous formulations (Doi, Doi-Peliti, RDME) as special cases, and demonstrate how it yields consistent multiscale numerical schemes and parameter relations across scales. Crucially, while the framework is grounded in reaction-diffusion systems, its structure is sufficiently general to extend to a wide range of complex systems — including population dynamics, neuroscience, and social systems — wherever agents interact and change in number, opening new avenues for multiscale modeling across disciplines.
