Scattering entanglement entropy between one particle species and the others
Abstract
We construct the entanglement entropy of a general scattering process between one particle species (denoted as A) and the rest of the final state. Assuming a pure initial momentum eigenstate, we show that the reduced density matrix in particle A's Fock space is block-diagonal in zero-, one- and multi-particle states, and is diagonal in the momentum basis for the one-particle state. As a result, we could write down the Von Neumann entropy of particle A, SA, in terms of scattering probabilities and differential cross sections, assuming no more than one particle A is produced in the final state. SA contains the information of both the total scattering probabilities (or cross sections) and the differential distributions --- the latter depends on a phase-space resolution factor as a result of the infinite-dimensional momentum Hilbert space. Our result is general and model-independent since we consider the full final state from time evolution (S|i⟩) rather than a specific outcome, and is applicable as long as the probability for producing multiple particle A is subleading. We also obtain the n≥2 Tsallis and Rényi entropies in our framework and find out that, at the leading order, they are proportional to the total scattering probability and carry no differential information.
Related
BibTeX
@misc{zheng2026scattering,
title = {{Scattering entanglement entropy between one particle species and the others}},
author = {Yuan-Hao Zheng and Jiayin Gu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10704},
eprint = {2610.10704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10704},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scattering entanglement entropy between one particle species and the others
AU - Yuan-Hao Zheng
AU - Jiayin Gu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10704
UR - https://arxiv.org/abs/2610.10704
AB - We construct the entanglement entropy of a general scattering process between one particle species (denoted as A) and the rest of the final state. Assuming a pure initial momentum eigenstate, we show that the reduced density matrix in particle A's Fock space is block-diagonal in zero-, one- and multi-particle states, and is diagonal in the momentum basis for the one-particle state. As a result, we could write down the Von Neumann entropy of particle A, S_A, in terms of scattering probabilities and differential cross sections, assuming no more than one particle A is produced in the final state. S_A contains the information of both the total scattering probabilities (or cross sections) and the differential distributions --- the latter depends on a phase-space resolution factor as a result of the infinite-dimensional momentum Hilbert space. Our result is general and model-independent since we consider the full final state from time evolution (S|i⟩) rather than a specific outcome, and is applicable as long as the probability for producing multiple particle A is subleading. We also obtain the n≥2 Tsallis and Rényi entropies in our framework and find out that, at the leading order, they are proportional to the total scattering probability and carry no differential information.
ER -