Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models

TL;DR

This paper establishes a connection between many-body particle imbalance dynamics and single-particle survival probabilities in quadratic models, supported by numerical tests on localization models, suggesting measurable links between single-particle and many-body observables.

Contribution

It demonstrates that many-body particle imbalance dynamics can reflect single-particle survival and transition probabilities in quadratic fermionic models, providing a new perspective on many-body dynamics.

Findings

Particle imbalance dynamics mirror single-particle survival probabilities.

Relationship extends to non-equal time and space density correlations.

Numerical validation on Anderson and Aubry-André models confirms the connection.

Abstract

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-Andr\'e 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.