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Quantum chaos and operator fidelity metric
1Institute for Scientific Interchange, Torino, Italy.
Summary
The operator fidelity metric, an information-theoretic measure, effectively distinguishes quantum chaotic behavior from regular behavior. This tool aids in understanding phase transitions in quantum systems.
Area of Science:
- Quantum chaos
- Information theory
- Statistical mechanics
Background:
- Investigating quantum chaotic behavior is crucial for understanding complex quantum systems.
- Existing methods for distinguishing regular and chaotic phases can be limited.
- Operator fidelity offers a novel approach to assess quantum system stability.
Purpose of the Study:
- To introduce and validate the operator fidelity metric as a tool for analyzing the transition to quantum chaos.
- To explore the utility of operator fidelity in discriminating between regular and quantum chaotic phases.
- To numerically investigate the onset of chaos in the Dicke model using operator fidelity.
Main Methods:
- Utilizing the operator fidelity metric, an information-theoretic measure of unitary evolution stability.
- Employing random matrix theory arguments to develop a conjecture for phase discrimination.
- Conducting numerical simulations on the Dicke model to test the conjecture.
Main Results:
- Operator fidelity serves as a natural and effective tool for studying the crossover to quantum chaotic behavior.
- The metric successfully discriminates between phases exhibiting regular dynamics and those demonstrating quantum chaos.
- Numerical results from the Dicke model support the conjecture regarding operator fidelity's discriminatory power.
Conclusions:
- Operator fidelity is a robust measure for identifying quantum chaotic regimes.
- This metric provides new insights into phase transitions in quantum systems.
- The findings pave the way for further applications of operator fidelity in quantum physics.
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