An Area Law for Entanglement Entropy in Particle Scattering

• URL: http://arxiv.org/abs/2405.08056v1
• Date: Mon, 13 May 2024 18:00:00 GMT
• Title: An Area Law for Entanglement Entropy in Particle Scattering
• Authors: Ian Low, Zhewei Yin,
• Abstract summary: We compute the entanglement entropy in 2-to-2 scattering of particles in a general setting. Since $sigma_textel$ is generally believed, and observed experimentally, to grow with the collision energy $sqrts$ in the high energy regime, the result suggests a "second law" of entanglement entropy for high energy collisions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The scattering cross section is the effective area of collision when two particles collide. Quantum mechanically, it is a measure of the probability for a specific process to take place. Employing wave packets to describe the scattering process, we compute the entanglement entropy in 2-to-2 scattering of particles in a general setting using the $S$-matrix formalism. Applying the optical theorem, we show that the linear entropy $\mathcal{E}_2$ is given by the elastic cross section $\sigma_{\text{el}}$ in unit of the transverse size $L^2$ of the wave packet, $\mathcal{E}_2 \sim \sigma_{\text{el}}/L^2$, when the initial states are not entangled. The result allows for dual interpretations of the entanglement entropy as an area and as a probability. Since $\sigma_{\text{el}}$ is generally believed, and observed experimentally, to grow with the collision energy $\sqrt{s}$ in the high energy regime, the result suggests a "second law" of entanglement entropy for high energy collisions. Furthermore, the Froissart bound places an upper limit on the entropy growth.

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