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Updated: May 31, 2026
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Published on: March 30, 2017
Fidelity decay in interacting two-level boson systems: freezing and revivals
Luis Benet1, Saúl Hernández-Quiroz, Thomas H Seligman
1Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM), Cuernavaca, México.
Summary
We investigated fidelity decay in quantum systems using random matrix theory. We found that fidelity can freeze and periodically revive, with revival periods linked to interaction range.
Area of Science:
- Quantum mechanics
- Statistical physics
- Quantum chaos
Background:
- Fidelity decay measures the stability of quantum states under perturbations.
- Random matrix theory (RMT) is used to model complex quantum systems.
- Embedded random matrix ensembles provide a more realistic framework for studying specific interactions.
Purpose of the Study:
- To analyze fidelity decay in k-body embedded ensembles of random matrices for bosons.
- To investigate the phenomenon of fidelity freeze and periodic revivals.
- To establish a relationship between revival periodicity and the interaction range (k).
Main Methods:
- Calculation of ensemble-averaged fidelity using linear response theory up to second order in perturbation strength.
- Analytical derivation of fidelity decay and revival behavior.
- Numerical simulations to confirm analytical predictions.
Main Results:
- Demonstration of a fidelity freeze phenomenon in the studied ensembles.
- Observation of periodic revivals in average fidelity at integer multiples of Heisenberg time (tH).
- Establishment that revival periodicity is an integer fraction of tH, dependent on the interaction range k.
Conclusions:
- The study reveals a connection between the range of interactions and the dynamics of quantum state stability.
- Fidelity freeze and revivals are characteristic features of these boson ensembles.
- The findings contribute to understanding quantum chaos and thermalization in interacting many-body systems.
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