Abstract
In a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states, i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.
Highlights
Since we are interested in a scattering process of two particles, A and B, and their entanglement, let us consider the Hamiltonian with an interaction:
While the sub-leading term in the case of the unentangled initial state is of order λ2, the sub-leading term in the case of the entangled initial state appears at order λ
We have studied the variation of entanglement entropy from an initial state to a final state in a scattering process
Summary
Since we are interested in a scattering process of two particles, A and B, and their entanglement, let us consider the Hamiltonian with an interaction:. We restrict the Hilbert space to the (1+1)-particle Fock space, in which the initial and final states are. The unitarity is approximately recovered at a weak coupling Under this assumption, we can divide the Hilbert space of the initial and final states to HA ⊗ HB, 2Ref. When one obtains a perturbative expansion of trAρnA, the term of order λn relevantly contributes to the entanglement entropy because the operation limn→1. Instead of the replica trick, we apply the perturbative method developed by Ref. [13] for calculating an entanglement entropy
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