Chaos and quantization of the three-particle generic Fermi-Pasta-Ulam-Tsingou model. II. Phenomenology of quantum eigenstates.

We undertake a thorough investigation into the phenomenology of quantum eigenstates, in the three-particle Fermi-Pasta-Ulam-Tsingou model. Employing different Husimi functions, our study focuses on both the α-type, which is canonically equivalent to the celebrated Hénon-Heiles Hamiltonian, a nonintegrable and mixed-type system, and the general case at the saddle energy where the system is fully chaotic. Based on Husimi quantum surface of sections, we find that in the mixed-type system, the fraction of mixed eigenstates in an energy shell [E-δE/2,E+δE/2] with δE≪E shows a power-law decay with respect to the decreasing Planck constant ℏ.

Chaos and quantization of the three-particle generic Fermi-Pasta-Ulam-Tsingou model. I. Density of states and spectral statistics.

We study the mixed-type classical dynamics of the three-particle Fermi-Pasta-Ulam-Tsingou (FPUT) model in relationship with its quantum counterpart and present new results on aspects of quantum chaos in this system. First we derive for the general N-particle FPUT system the transformation to the normal mode representation. Then we specialize to the three-particle FPUT case and derive analytically the semiclassical energy density of states, and its derivatives in which different singularies are determined, using the Thomas-Fermi rule.

Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit.

How the mixed eigenstates vary when approaching the semiclassical limit in mixed-type many-body quantum systems is an interesting but still less known question. Here, we address this question in the Dicke model, a celebrated many-body model that has a well defined semiclassical limit and undergoes a transition to chaos in both quantum and classical cases. Using the Husimi function, we show that the eigenstates of the Dicke model with mixed-type classical phase space can be classified into different types.

Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space.

The properties of mixed eigenstates in a generic quantum system with a classical counterpart that has mixed-type phase space, although important to understand several fundamental questions that arise in both theoretical and experimental studies, are still not clear. Here, following a recent work [Č. Lozej, D.

Quantum Chaos-Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday.

Quantum chaos is the study of phenomena in the quantum domain which correspond to classical chaos [...