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Updated: Aug 12, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Fractional-order quantum kicked top map and its discrete dynamic behaviors
Ze-Yu Liu1, Tie-Cheng Xia2, Ting-Ting Wang1
1College of Science, Northwest A&F University, Yangling District, Xianyang, Shaanxi 712100, People's Republic of China.
This study introduces a fractional quantum kicked top model with a Caputo derivative, revealing chaotic dynamics through numerical simulations. The research analyzes fractional quantum dynamics in a finite Hilbert space.
Area of Science:
- Quantum mechanics
- Nonlinear dynamics
- Fractional calculus
Background:
- The quantum kicked top model is a standard model for studying quantum chaos.
- Investigating fractional dynamics offers new insights into complex systems.
Purpose of the Study:
- To propose and analyze a fractional quantum kicked top map using the Caputo derivative.
- To explore the chaotic behaviors and quantum dynamics of this fractional model.
Main Methods:
- Developing a fractional quantum kicked top map based on the Caputo derivative.
- Obtaining numerical solutions for the fractional difference equation.
- Analyzing dynamic behaviors using bifurcation diagrams, phase diagrams, and maximum Lyapunov exponents.
Main Results:
- Numerical solutions demonstrate chaotic behavior in the fractional quantum kicked top map.
- Fractional quantum dynamics are observed within a finite-dimensional Hilbert space.
- Systematic analysis confirms the presence of chaos through various dynamical indicators.
Conclusions:
- The fractional quantum kicked top map exhibits complex and chaotic dynamics.
- This model provides a framework for studying fractional quantum chaos.
- The findings contribute to understanding nonlinear dynamics in quantum systems.
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