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Dynamics of quasiperiodically driven spin systems.

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We explore spin dynamics under Fibonacci-generated magnetic fields. Despite chaotic classical behavior, quantum coherence persists, revealing fractal fluctuations and potential thermalization with interactions.

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Area of Science:

  • Quantum dynamics
  • Spin physics
  • Chaos theory

Background:

  • Investigating spin dynamics in magnetic fields is crucial for quantum technologies.
  • The Fibonacci sequence offers a unique, non-trivial pattern for field generation.
  • Understanding classical-quantum transitions in chaotic systems is a fundamental challenge.

Purpose of the Study:

  • To analyze the stroboscopic dynamics of a spin-S object under a Fibonacci-generated transverse magnetic field.
  • To construct and study the classical Hamiltonian map in the large spin limit (S→∞).
  • To examine the quantum dynamics, phase coherence, and fractal properties of spin operators and Floquet eigenstates.

Main Methods:

  • Construction of a classical Hamiltonian map for large spin (S→∞).
  • Analysis of classical phase space for chaotic behavior and Lyapunov exponent calculation.
  • Derivation of the Sutherland invariant for SO(3) matrix dynamics.
  • Study of quantum phase coherence and spin operator fluctuations.
  • Investigation of system behavior with inter-spin interactions.

Main Results:

  • Classical phase space exhibits apparent chaos, yet the Lyapunov exponent remains zero, indicating linear geodesic distance increase.
  • Quantum phase coherence is maintained during time evolution.
  • Fluctuations in mean spin operator values display fractal characteristics, mirrored in Floquet eigenstates.
  • Inter-spin interactions induce ergodic dynamics, leading to infinite temperature thermalization.

Conclusions:

  • The system demonstrates a unique blend of classical chaos and quantum stability.
  • Fractal properties in quantum fluctuations and eigenstates are key findings.
  • Interactions drive the system towards thermalization, highlighting the role of ergodicity.