Erratum: Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability [Phys. Rev. Lett. 128, 134102 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.134102.

Thermalization dynamics of macroscopic weakly nonintegrable maps.

We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity, the almost conserved actions correspond to extended observables which are coupled into a long-range network. For weakly connected lattices, the corresponding local observables are coupled into a short-range network. We compute the evolution of the variance σ ( T ) of finite time average distributions for extended and local observables. We extract the ergodization time scale T which marks the onset of thermalization, and determine the type of network through the subsequent decay of σ ( T ). We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time T with T. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.

Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability.

We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate macroscopic weakly nonintegrable dynamics beyond the limits set by the KAM regime. We perform our analysis in two fundamentally distinct long-range and short-range integrable limits which stem from the type of nonintegrable perturbations. Long-range limits result in a single parameter scaling of the Lyapunov spectrum, with the inverse largest Lyapunov exponent being the only diverging control parameter and the rescaled spectrum approaching an analytical function. Short-range limits result in a dramatic slowing down of thermalization which manifests through the rescaled Lyapunov spectrum approaching a non-analytic function. An additional diverging length scale controls the exponential suppression of all Lyapunov exponents relative to the largest one.

All-phononic amplification in coupled cantilever arrays based on gap soliton dynamics.

We present a mechanism of amplification of phonons by phonons on the basis of nonlinear band-gap transmission phenomenon. As a concept the idea may be applied to the various number of systems; however we introduce the specific idea of creating an amplification scenario in the chain of coupled cantilever arrays. One chain is driven at the constant frequency located in the upper band of the ladder system, thus no wave enters the system. However the frequency is specifically chosen to be very close to the maximum value of the frequency corresponding to the dispersion relation of the system. An amplification scenario happens when a counter phase pulse of the same frequency with a small amplitude is introduced to the second chain. If both signals exceed a threshold amplitude for the band-gap transmission a large amplitude soliton enters the system-therefore we have an amplifier. Although the concept may be applied in a variety of contexts, all-optical or all-magnonic systems, we choose the system of coupled cantilever arrays and represent a clear example of the application of the presented conceptual idea. Logical operations is the other probable field, where such a mechanism could be used, which might significantly broaden the horizon of the considered applications of band-gap soliton dynamics.

All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder.

A conceptual mechanism of amplification of phonons by phonons on the basis of a nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example, a system of weakly coupled chains of anharmonic oscillators is considered. One (source) chain is driven harmonically by a boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counterphase and with the same frequency as the first chain. If the total driving of both chains overcomes the band-gap transmission threshold, the large amplitude band-gap soliton emerges and the amplification scenario is realized. The mechanism is interpreted as the nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or bandpass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and have all the promise of logic gate operations.