The reduced effect of a single scattering with a low-mass particle via a point interaction

الأصل · EN

In this article, we study a second-order expansion for the effect induced on a large quantum particle which undergoes a single scattering with a low-mass particle via a repulsive point interaction. We give an approximation with third-order error in λ to the map G→ ₂[(I⊗ ρ)Sλ*(G⊗ I)Sλ], where G∈ (L²(ⁿ)) is a heavy-particle observable, ρ∈ ₁(ⁿ) is the density matrix corresponding to the state of the light particle, λ=m/M is the mass ratio of the light particle to the heavy particle, Sλ∈ (L²(ⁿ)⊗ L²(ⁿ)) is the scattering matrix between the two particles due to a repulsive point interaction, and the trace is over the light-particle Hilbert space. The third-order error is bounded in operator norm for dimensions one and three using a weighted operator norm on G.