Monteoliva Diana, Plastino Angelo, Plastino Angel Ricardo
UNLP-Comisión de Investigaciones Científicas Provincia de Buenos Aires, La Plata 1900, Argentina.
Instituto de Física La Plata, CCT-CONICET, Universidad Nacional de La Plata, La Plata 1900, Argentina.
Entropy (Basel). 2025 Jan 6;27(1):37. doi: 10.3390/e27010037.
In this study, we utilize information theory tools to investigate notable features of the quantum degree of mixedness (Cf) in a finite model of interacting fermions. This model serves as a simplified proxy for an atomic nucleus, capturing its essential features in a more manageable form compared to a realistic nuclear model, which would require the diagonalization of matrices with millions of elements, making the extraction of qualitative features a significant challenge. Specifically, we aim to correlate Cf with particle number fluctuations and temperature, using the paradigmatic Lipkin model. Our analysis reveals intriguing dependencies of Cf on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion-fermion interaction (as long as it is non-zero), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs depicting these dependencies, offering valuable insights into the fundamental characteristics of quantum many-body fermion systems. Our findings illuminate the intricate dynamics of the degree of mixedness, a crucial quantum property, with potential implications for diverse fields ranging from condensed matter physics to quantum information science.
在本研究中，我们利用信息论工具来研究相互作用费米子有限模型中量子混合度（Cf）的显著特征。该模型作为原子核的简化替代物，与现实的核模型相比，以更易于处理的形式捕捉了其基本特征，现实的核模型需要对包含数百万个元素的矩阵进行对角化，这使得提取定性特征成为一项重大挑战。具体而言，我们旨在使用典型的李普金模型将Cf与粒子数涨落和温度联系起来。我们的分析揭示了Cf对总费米子数的有趣依赖性，展示了在不同温度下的不同行为。值得注意的是，我们发现量子混合度对总费米子数表现出强烈依赖性，在不同温度区间有不同趋势。值得注意的是，这种依赖性不受费米子 - 费米子相互作用强度的影响（只要它不为零），这突出了所观察到现象的稳健性。通过全面的数值模拟，我们提供了描述这些依赖性的说明性图表，为量子多体费米子系统的基本特征提供了有价值的见解。我们的发现阐明了混合度这一关键量子性质的复杂动力学，对从凝聚态物理到量子信息科学等多个领域都有潜在影响。
