We study phonon relaxation in chains of particles coupled through polynomial-type pair-interaction potentials and obeying quantum dynamics. We present detailed calculations for the sixth-order potential and find that the wave-vector-dependent relaxation rate follows a power-law behavior, $\ensuremath{\Gamma}(q)\ensuremath{\sim}{q}^{\ensuremath{\delta}}$, with $\ensuremath{\delta}=5/3$, which is identical to that of the fourth-order potential. We argue through diagrammatic analysis that this is a generic feature of even-power potentials. Our earlier analysis has shown that $\ensuremath{\delta}=3/2$ when the leading-order term in the nonlinear potential is odd, suggesting that there are two universality classes for the phonon relaxation rates dependent on a simple property of the potential. This implies that the thermal conductivity $\ensuremath{\kappa}$ which diverges as a function of chain size
N as $\ensuremath{\kappa}\ensuremath{\propto}{N}^{\ensuremath{\alpha}}$ also has two universal behaviors, in that $\ensuremath{\alpha}=1\ensuremath{-}1/\ensuremath{\delta}$ as follows from a finite-size argument. We support these arguments by numerical calculations of conductivity for chains obeying classical dynamics for polynomial potentials of some even and odd powers.
Energy equipartition can be established in short-range systems after the dynamic process of thermalization. However, energy distribution between different degrees of freedom in systems with long-range interactions is unclear. We study the dynamics of energy relaxation in the Fermi-Pasta-Ulam-Tsingou β model with long-range quartic interactions, which decay as 1/d^{δ} with d being the lattice distance. The dynamic crossover of a mode-energy distribution from localized to equipartitioned with the increase of the power δ is observed. A transition of mode-energy distribution is identified around the value of δ=1, which usually serves as the distinction between strong and weak long-range couplings. We elucidate that the varying frequency overlapping of the mode-energy power spectrum is responsible for this dynamic crossover. Through further calculation of the spectral entropy, the minimum duration of quasistationary states, τ_{QSS}, is found at δ=2, which may provide possible dynamic explanations for the peculiar behavior of heat transport in long-range lattice chains. In addition, the double scaling in τ_{QSS} as a function of energy density is also observed in our long-range lattices. Our results not only contribute to understanding the dynamics of energy relaxation in long-range systems, but also shed light on the longstanding problem of thermalization and low-dimensional heat transport in short-range systems.
Abstract We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi–Pasta–Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power of the inverse of their distance. The structure factors at finite energy density display distinct peaks, corresponding to long-wavelength propagating modes, whose dispersion relation is compatible with the predictions of the linear theory. We demonstrate that dynamical scaling holds, with a dynamical exponent z that depends weakly on in the range . The lineshapes have a non-trivial functional form and appear somehow independent of . Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of .
In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron–phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron–lattice interaction promote a sub-diffusive electronic dynamics.
The Fermi--Pasta--Ulam--Tsingou (FPUT) problem provides a paradigmatic framework for understanding thermalization in weakly nonlinear many-body Hamiltonian systems. This focused review summarizes major developments in near-integrable dynamics, wave resonances, and phonon kinetic theory, emphasizing recent results on thermalization-time scaling in nonlinear lattices. A coherent picture emerges in the thermodynamic limit based on the eigenmode properties of an appropriate integrable reference system. If the reference system has extended eigenmodes and the leading resonant or quasi-resonant processes form a sufficiently connected network, the thermalization time follows
Teq∝g−2, where
g measures the effective deviation from integrability. This scaling is found broadly in ordered and weakly disordered lattices and is robust to dimensionality, interaction potential, integrability-breaking mechanism, and multimode initial conditions. Identifying the correct integrable reference is essential; in some one-dimensional FPUT-type lattices with cubic interactions, the nearby Toda lattice, rather than the harmonic chain, provides the proper reference. If all reference eigenmodes are localized, spatial-overlap constraints progressively fragment low-order resonance networks as
g decreases, and thermalization becomes controlled by higher-order processes. Numerical studies reveal successive regimes
Teq∝g−γ with
γ=2,4,6, together with weak system-size dependence. Whether this hierarchy persists asymptotically and whether a finite thermalization threshold exists remain open questions. We also discuss finite-size effects, strongly nonintegrable dynamics, heat transport, localization, and higher-dimensional lattices.
We perform a series of numerically accurate tensor-train (TT) simulations of population dynamics and energy transfer in quantum β-Fermi-Pasta-Ulam-Tsingou (FPUT) chains comprising 10 to 30 nonlinear oscillators. The dynamics are propagated over timescales ranging from 18 to 60 fundamental vibrational periods. We demonstrate that the chain anharmonicity opens new energy-transfer channels, accelerates initial ballistic energy propagation, reduces (partial) recurrence periods relative to the harmonic limit, and regularizes oscillatory wavepacket motion. This work serves as the first proof-of-principle demonstration of the high efficiency of TT methods for simulating quantum FPUT dynamics.