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We consider a physical system with a coupling to bosonic reservoirs via aquantum stochastic differential equation. We study the limit of this model asthe coupling strength tends to infinity. We show that in this limit thesolution to the quantum stochastic differential equation converges strongly tothe solution of a limit quantum stochastic differential equation. In thelimiting dynamics the excited states are removed and the ground states coupledirectly to the reservoirs.

Adiabatic elimination in quantum stochastic models