arXiv 2405.080562024-05-13hep-thcond-mat.stat-mechhep-phnucl-thquant-ph

粒子散射中纠缠熵的面积定律

An Area Law for Entanglement Entropy in Particle Scattering

Ian Low, Zhewei Yin

备注：: 5 pages + Supplementary Material, 1 figure

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AI总结：

该研究利用S矩阵形式计算粒子2对2散射的纠缠熵，证明线性熵与弹性截面满足面积律关系，提出高能碰撞纠缠熵第二定律，并指出弗罗萨尔界为熵增长设上限。

摘要：

散射截面是两个粒子碰撞时的有效碰撞面积。在量子力学中，它是特定过程发生概率的量度。我们采用波包描述散射过程，利用S矩阵（S-matrix）形式体系，在一般设定下计算了粒子2对2散射中的纠缠熵。应用光学定理，我们证明当初始态未纠缠时，线性熵$\u2130_2$由弹性截面$σ_{\text{el}}$以波包横向尺寸$L^2$为单位给出，即$\u2130_2 \u223c σ_{\text{el}}/L^2$。该结果使得纠缠熵可同时具有面积和概率的双重解释。由于普遍认为且实验观测到，在高能区弹性截面$σ_{\text{el}}$随碰撞能量$\u221as$增长，该结果暗示高能碰撞存在纠缠熵的“第二定律”。此外，弗罗萨尔界（Froissart bound）为熵的增长设定了上限。

英文摘要：

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.

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