We develop a unified Hamiltonian approach to the diffusion of a particle coupled to a dissipative environment, an archetypal model widely invoked to interpret condensed phase phenomena, such as polymerization and cold-atom diffusion in optical lattices. By appropriate choices of the coupling functions, we reformulate phenomenological diffusion models by adding otherwise ignored space-momentum terms. We thus numerically predict a variety of diffusion regimes, from diffusion saturation to superballistic diffusion. With reference to ultracold atoms in optical lattices, we also show that time correlated external noises prevent superdiffusion from exceeding Richardson's law. Some of these results are unexpected and call for experimental validation.

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• Diffusion
• Fluctuation theorems
• Growth processes
• Nonequilibrium statistical mechanics