Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
Abstract
:1. Introduction
2. Models
3. Survival Probability and Particle Imbalance
4. Transition Probabilities and Density Correlation Functions (Generalized Imbalance)
5. Equal Time Connected Density–Density Correlation Functions
6. Discussion
- (i)
- We relate the dynamics of particle imbalance to the dynamics of single-particle survival probability, and we show that the two become nearly indistinguishable.
- (ii)
- We extend the result (i) by showing that the generalized imbalance, i.e., the non-equal time and space density correlation function, also becomes nearly indistinguishable from the single-particle transition probabilities. Results (i) and (ii) give a recipe for experiments on how to measure the properties of survival and transition probabilities using one-body observables.
- (iii)
- We discuss the other experimentally relevant observables, i.e., the equal-time connected density–density correlation functions, which can be related to the one-particle density matrix observables. We showed that these observables have qualitative, but not quantitative, similarities with the survival and transition probabilities. Importantly, they also appear to exhibit the scale-invariant dynamics at localization transitions; thus, they constitute an alternative route for the experimental observation of critical dynamics.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. System Size Dependence of Differences between P(d) and C(d)
Appendix B. Rescaled Imbalance and Transition Probabilities: Scale-Invariant Dynamics at Eigenstate Transitions
Appendix C. Equal-Time Connected Density–Density Correlation Functions: Scale-Invariant Dynamics at Eigenstate Transitions
Appendix D. Connection to Fractal Dimension
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Hopjan, M.; Vidmar, L. Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models. Entropy 2024, 26, 656. https://doi.org/10.3390/e26080656
Hopjan M, Vidmar L. Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models. Entropy. 2024; 26(8):656. https://doi.org/10.3390/e26080656
Chicago/Turabian StyleHopjan, Miroslav, and Lev Vidmar. 2024. "Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models" Entropy 26, no. 8: 656. https://doi.org/10.3390/e26080656