An infinite-temperature limit for a quantum scattering process

We study a quantum dynamical semigroup driven by a Lindblad generator with a deterministic Schrödinger part and a noisy Poisson-timed scattering part. The dynamics describes the evolution of a test particle in ℝn, n = 1, 2, 3, immersed in a gas, and the noisy scattering part is defined by the reduced effect of an individual interaction, where the interaction between the test particle and a single gas particle is via a repulsive point potential. In the limit that the mass ratio λ = m/M tends to zero and the collisions become more frequent as 1/λ, we show that our dynamics Φtλ◊ approaches a limiting dynamics Φt,λ with second order error. Working in the Heisenberg representation, for G ∈ B(L2(ℝn)) n = 1, 3 we bound the difference between Φt,λ(G) and Φt,λ◊(G) in operator norm proportional to λ2.