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Transition from order to chaos in reduced quantum dynamics
Waldemar Kłobus1, Paweł Kurzyński2, Marek Kuś3
1Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland.
Physical Review. E
|April 16, 2022
Summary
We investigated quantum kicked top dynamics in a large qubit system. A universal period-doubling behavior was observed as damping increased, characteristic of chaotic systems.
Area of Science:
- Quantum Information Science
- Quantum Chaos
- Quantum Dynamics
Background:
- The kicked top model is a paradigmatic model for studying quantum chaos.
- Understanding the transition from regular to chaotic dynamics in quantum systems is a key challenge.
- Investigating the role of dissipation in quantum chaotic systems is crucial for realistic applications.
Purpose of the Study:
- To explore the dynamics of a damped kicked top model for a large number of qubits (N→∞).
- To analyze the evolution of a reduced single-qubit subsystem under amplitude damping.
- To identify universal behaviors and bifurcations in the quantum chaotic regime.
Main Methods:
- Simulation of a large qubit system (N→∞) undergoing damped kicked top dynamics.
- Focus on the evolution of a reduced single-qubit subsystem subjected to an amplitude damping channel.
- Analysis of the control parameter (damping constant r) and its effect on system dynamics.
Main Results:
- Observed universal period-doubling behavior characteristic of one-dimensional maps in the chaotic regime.
- Identified critical damping constants for period-doubling bifurcations (r₁≈0.3181, r₂≈0.5387).
- Discovered a secondary bifurcation diagram around r≈0.544, leading to small-scale chaos, and noted the onset of full-scale chaos at r∞∼0.578.
Conclusions:
- The damped kicked top model exhibits universal period-doubling bifurcations analogous to classical chaotic systems.
- Dissipation introduces rich dynamics, including secondary bifurcations and windows of oscillatory behavior within the chaotic regime.
- The study provides insights into the interplay between quantum chaos and dissipation in multi-qubit systems.
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