二次模型中的生存概率、粒子不平衡及其关系
Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
AI总结：
本文证明二次费米子模型中多体粒子不平衡动力学与单粒子生存概率几乎不可区分，并推广到密度关联函数与跃迁概率的关系，在Anderson和Aubry-André模型上验证了通过多体可观测量测量单粒子概率特征的可能性。
摘要：
我们认为，在二次费米子模型中，对于位点占据基下的大多数初始多体乘积态，粒子不平衡的动力学实际上与单粒子态生存概率的动力学几乎无法区分。随后，我们将这一陈述推广到多体态中的非等时和空间密度关联函数与单粒子态在非零距离处的跃迁概率之间的类似关系。最后，我们研究了多体态中的等时连通密度-密度关联函数，它们表现出与单粒子态的生存概率和跃迁概率的某些定性类比。我们的结果在两个单粒子局域化的典型模型上进行了数值检验：3D Anderson模型和1D Aubry-André模型。这项工作对是否可能通过多体态中可观测量的动力学来测量单粒子生存概率和跃迁概率的特征这一问题给出了肯定的回答。
英文摘要：
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal time connected density-density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry-André model. This work gives affirmative answer to the question whether it is possible to measure features of the single-particle survival and transition probabilities by the dynamics of observables in many-body states.
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