4.8 Article

Exploring Integrability-Chaos Transition with a Sequence of Independent Perturbations

Journal

PHYSICAL REVIEW LETTERS
Volume 130, Issue 2, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.130.020404

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This study investigates the chaotic properties of interacting particles. Even if all particles except one are fixed, the excited states of the moving particle are still chaotic. These states are characterized by the number of principal components (NPC), which increases in a linear manner with the number of strong scatterers. The effect of additional perturbation on the chaotic properties of the system is examined, and the decay of observable fluctuation variance is observed as an indicator of approaching eigenstate thermalization.
A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that, even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by the number of principal components (NPC)-the number of integrable system eigenstates involved into the nonintegrable one, which increases linearly with the number of strong scatterers. This rule is a particular case of the general effect of an additional perturbation on the system chaotic properties. The perturbation independence criteria supposing the system chaoticity increase are derived here as well. The effect can be observed in experiments with photons or cold atoms as the decay of observable fluctuation variance, which is inversely proportional to NPC and, therefore, to the number of scatterers. This decay indicates that the eigenstate thermalization is approached. The results are confirmed by numerical calculations for a harmonic waveguide with zero-range scatterers along its axis.

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