We study the transition from integrability to chaos for the three-particle Fermi-Pasta-Ulam-Tsingou (FPUT) model. We can show that both the quartic beta-FPUT model (alpha=0) and the cubic one (beta=0) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of alpha and beta, the model is non-integrable and displays a mixed phase space with both chaotic and regular trajectories. In the classical case, chaos is diagnosed by the investigation of Poincare sections. In the quantum case, the level spacing statistics in the energy basis belongs to the Gaussian orthogonal ensemble in the chaotic regime, and crosses over to Poissonian behavior in the quasi-integrable low-energy limit. In the chaotic part of the spectrum, two generic observables obey the eigenstate thermalization hypothesis.

Quantization of Integrable and Chaotic Three-Particle Fermi-Pasta-Ulam-Tsingou Models / Arzika, Alio Issoufou; Solfanelli, Andrea; Schmid, Harald; Ruffo, Stefano. - In: ENTROPY. - ISSN 1099-4300. - 25:3(2023), pp. 1-13. [10.3390/e25030538]

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

Solfanelli, Andrea;Ruffo, Stefano
2023-01-01

Abstract

We study the transition from integrability to chaos for the three-particle Fermi-Pasta-Ulam-Tsingou (FPUT) model. We can show that both the quartic beta-FPUT model (alpha=0) and the cubic one (beta=0) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of alpha and beta, the model is non-integrable and displays a mixed phase space with both chaotic and regular trajectories. In the classical case, chaos is diagnosed by the investigation of Poincare sections. In the quantum case, the level spacing statistics in the energy basis belongs to the Gaussian orthogonal ensemble in the chaotic regime, and crosses over to Poissonian behavior in the quasi-integrable low-energy limit. In the chaotic part of the spectrum, two generic observables obey the eigenstate thermalization hypothesis.
2023
25
3
1
13
538
10.3390/e25030538
https://www.mdpi.com/1099-4300/25/3/538
https://arxiv.org/abs/2303.17577
Arzika, Alio Issoufou; Solfanelli, Andrea; Schmid, Harald; Ruffo, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/132092
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