Chaotic Dynamics in a Quantum Fermi-Pasta-Ulam Problem

Two stage decoherence of optical phonons in long oligomers

Molecular vibrations are generally responsible for chemical energy transport and dissipation in molecular systems. This transport is fast and efficient if energy is transferred by optical phonons in periodic oligomers, but its efficiency is limited by decoherence emerging due to anharmonic interactions with acoustic phonons. Using a general theoretical model, we show that in the most common case of the optical phonon band being narrower than the acoustic bands, decoherence takes place in two stages. The faster stage involves optical phonon multiple forward scattering due to absorption and emission of transverse acoustic phonons, i.e., collective bending modes with a quadratic spectrum; the transport remains ballistic and the speed can be altered. The subsequent slower stage involves phonon backscattering in multiphonon processes involving two or more acoustic phonons resulting in a switch to diffusive transport. If the initially excited optical phonon possesses a relatively small group velocity, then it is accelerated in the first stage due to its transitions to states propagating faster. This theoretical expectation is consistent with the recent measurements of optical phonon transport velocity in alkane chains, increasing with increasing the chain length.

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. The result agrees with the numerical energy density from the Krylov subspace method, as well as with the energy density obtained by the method of quantum typicality. Here, in paper I, we concentrate on the energy level statistics (level spacing and spacing ratios), in all classical dynamical regimes of interest: the almost entirely regular, the entirely chaotic, and the mixed-type regimes. We clearly confirm, correspondingly, the Poissonian statistics, the Gaussian orthogonal ensemble statistics, and the Berry-Robnik-Brody (BRB) statistics in the mixed-type regime. It is found that the BRB level spacing distribution perfectly fits the numerical data. The extracted quantum Berry-Robnik parameter is found to agree with the classical value within better than one percent. We discuss the role of localization of chaotic eigenstates, and its appearances, in relation to the classical phase space structure (Poincaré and smaller alignment index plots), whose details will be presented in paper II, where the structure and the statistical properties of the Husimi functions in the quantum phase space will be studied.

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

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 β-FPUT model (α=0) and the cubic one (β=0) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of α and β, 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 Poincaré 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.

Structural localization in the classical and quantum Fermi-Pasta-Ulam model

We study the statistics and short-time dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in the thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At low temperatures, we observe a systematic increase in the mobility of the chain when transitioning from classical to quantum mechanics due to zero-point energy effects. We analyze the consequences of quantum dispersion on the dynamics at short times of configurational correlation functions.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.