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Applications of fidelity measures to complex quantum systems
1Dipartimento di Fisica e Scienze della Terra, Università di Parma, Via G.P. Usberti 7/a, 43124 Parma, Italy INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Italy Institut für Theoretische Physik, Philosophenweg 12, Universität Heidelberg, 69120 Heidelberg, Germany sandromarcel.wimberger@unipr.it.
Summary
We introduce static and dynamical fidelity to measure quantum system stability and complexity. These methods effectively detect complex behaviors in cold atom systems and quantum dynamics, like in the kicked rotor model.
Area of Science:
- Quantum mechanics
- Atomic physics
- Statistical mechanics
Background:
- Fidelity is a crucial metric for assessing quantum system stability and complexity.
- Understanding quantum motion in single- and many-body systems is vital.
- Cold atom systems provide a controllable platform for studying quantum phenomena.
Purpose of the Study:
- To revisit and apply fidelity as a measure for quantum system stability and complexity.
- To present applications of static and dynamical fidelity in cold atom systems.
- To explore the utility of fidelity in characterizing complex quantum dynamics.
Main Methods:
- Definition and application of static fidelity using eigenfunctions for diagonalizable quantum systems.
- Definition and application of dynamical fidelity using time-dependent wave functions.
- Analysis of the quantum kicked rotor system to demonstrate fidelity applications.
Main Results:
- Static fidelity serves as a practical detector of avoided crossings, revealing system complexity.
- Dynamical fidelity, applied to the quantum kicked rotor, elucidates diverse dynamical regimes.
- Fidelity measurements offer insights into the mixed regular-chaotic phase space of low-dimensional systems.
Conclusions:
- Fidelity is a versatile tool for quantifying quantum system complexity and stability.
- Static and dynamical fidelity provide complementary insights into quantum system behavior.
- The quantum kicked rotor serves as an excellent model for demonstrating the power of fidelity measurements in exploring quantum dynamics.
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