Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
arxiv(2024)
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-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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