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General relation between quantum ergodicity and fidelity of quantum dynamics
1Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
Summary
Quantum dynamics fidelity, measuring stability to Hamiltonian variations, depends on ergodicity. Ergodic systems show exponential decay, while nonergodic systems exhibit faster Gaussian decay, as demonstrated in a quantum Ising chain.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter physics
Background:
- Quantum dynamics fidelity quantifies the stability of a quantum system's time evolution under small perturbations.
- Understanding the relationship between fidelity, ergodicity, and system dynamics is crucial for quantum information science and condensed matter theory.
Purpose of the Study:
- To derive a general relation connecting quantum dynamics fidelity with the ergodicity of the perturbing observable.
- To predict distinct fidelity decay behaviors for ergodic versus nonergodic quantum dynamics.
- To experimentally validate these predictions in a realistic quantum system.
Main Methods:
- Derivation of a general analytical relation for quantum fidelity.
- Analysis of fidelity decay rates based on system dynamics (ergodic vs. nonergodic).
- Numerical and/or experimental demonstration using a periodically kicked quantum Ising spin chain.
Main Results:
- A universal relation is established between fidelity decay and the ergodicity of the perturbation-generating observable.
- Ergodic dynamics predict exponential fidelity decay (proportional to delta^(-2)), while nonergodic dynamics predict faster Gaussian decay (proportional to delta^(-1)).
- Demonstrated regions of nonergodic, nonintegrable motion in the thermodynamic limit of the quantum Ising model.
Conclusions:
- Quantum dynamics fidelity is a sensitive probe of ergodicity and integrability.
- The derived fidelity decay laws provide a powerful tool for characterizing quantum chaos and thermalization.
- The findings open avenues for controlling quantum information and understanding complex quantum systems.