An Area Law for Entanglement Entropy in Particle Scattering
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909201119313920 |
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| author | Low, Ian Yin, Zhewei |
| author_facet | Low, Ian Yin, Zhewei |
| contents | 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 $σ_{\text{el}}$ in unit of the transverse size $L^2$ of the wave packet, $\mathcal{E}_2 \sim σ_{\text{el}}/L^2$, 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 $σ_{\text{el}}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Area Law for Entanglement Entropy in Particle Scattering Low, Ian Yin, Zhewei High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology Nuclear Theory Quantum Physics 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 $σ_{\text{el}}$ in unit of the transverse size $L^2$ of the wave packet, $\mathcal{E}_2 \sim σ_{\text{el}}/L^2$, 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 $σ_{\text{el}}$ 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. |
| title | An Area Law for Entanglement Entropy in Particle Scattering |
| topic | High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.08056 |