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Quantization of Integrable and Chaotic Three-Particle Fermi-Pasta-Ulam-Tsingou Models.

Alio Issoufou Arzika1,2, Andrea Solfanelli2,3, Harald Schmid4

  • 1LCEMR, Faculty of Science and Technology, Abdou Moumouni University, Niamey BP 10662, Niger.

Entropy (Basel, Switzerland)
|March 29, 2023
PubMed
Summary
This summary is machine-generated.

We investigated the Fermi-Pasta-Ulam-Tsingou (FPUT) model

Keywords:
chaotic Hamiltonian systemseigenstate thermalization hypothesisintegrable systemsquantum chaos

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Area of Science:

  • Nonlinear dynamics
  • Quantum chaos
  • Statistical mechanics

Background:

  • The Fermi-Pasta-Ulam-Tsingou (FPUT) model is a fundamental system for studying nonlinear dynamics and the transition to chaos.
  • Understanding the integrability and chaotic behavior of the FPUT model is crucial for various fields, including physics and mathematics.

Purpose of the Study:

  • To analyze the transition from integrability to chaos in the three-particle FPUT model.
  • To characterize the chaotic and regular dynamics in both classical and quantum regimes.

Main Methods:

  • Utilized a Fourier representation to demonstrate the integrability of specific FPUT model variants (quartic and cubic).
  • Employed Poincaré sections for diagnosing chaos in the classical FPUT model.
  • Analyzed level spacing statistics in the quantum FPUT model to identify chaotic and integrable regimes.

Main Results:

  • Identified integrable conditions for the cubic and quartic FPUT models.
  • Observed a mixed phase space with both chaotic and regular trajectories for generic parameter values.
  • Quantum analysis revealed Gaussian orthogonal ensemble statistics in the chaotic regime and Poissonian behavior in the quasi-integrable limit.
  • Demonstrated that two generic observables in the chaotic spectrum adhere to the eigenstate thermalization hypothesis.

Conclusions:

  • The three-particle FPUT model exhibits a clear transition from integrability to chaos.
  • The study provides a comprehensive characterization of the model's dynamics across classical and quantum domains.
  • Results align with established theories of quantum chaos and thermalization.