arXiv subjects

Merab Malishava

Publications and source records attributed to Merab Malishava.

6 recordsLinked to original sources

arXiv2022

Thermalization of Classical Weakly Nonintegrable Many-Body Systems

We devote our studies to the subject of weakly nonintegrable dynamics of systems with a macroscopic number of degrees of freedom. Our main points of interest are the relations between the timescales of thermalization and the timescales of chaotization; the choice of appropriate observables and the structure of equations coupling them; identifying the classes of weakly nonintegrable dynamics and developing tools to diagnose the properties specific to such classes. We discuss the traditional in the field methods for thermalization timescale computation and employ them to study the scaling the timescale with the proximity to the integrable limit. We then elaborate on a novel framework based on the full Lyapunov spectra computation for large systems as a powerful tool for the characterization of weak nonintegrability. In particular, the Lyapunov spectrum scaling offers a quantitative description allowing us to infer the structure of the underlying network of observables. Proximity to integrable limit is associated with the rapid growth of thermalization timescales and, thus, potential numerical challenges. We solve these challenges by performing numerical tests using computationally efficient model - unitary maps. The great advantage of unitary maps for numerical applications is time-discrete error-free evolution. We use these advantages to perform large timescale and system size computations in extreme proximity to the integrable limit. To demonstrate the scope of obtained results we report on the application of the developed framework to Hamiltonian systems.

nlin.CD↗

arXiv2022

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 $\sigma^2(T)$ of finite time average distributions for extended and local observables. We extract the ergodization time scale $T_E$ which marks the onset of thermalization, and determine the type of network through the subsequent decay of $\sigma^2(T)$. We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time $T_{\Lambda}$ with $T_E$. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.

nlin.CD↗

arXiv2021

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.

nlin.CD↗

arXiv2019

Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks

We study the interplay of two interacting discrete time quantum walks in the presence of disorder. Each walk is described by a Floquet unitary map defined on a chain of two-level systems. Strong disorder induces a novel Anderson localization phase with a gapless Floquet spectrum and one unique localization length $\xi_1$ for all eigenstates for noninteracting walks. We add a local contact interaction which is parametrized by a phase shift $\gamma$. A wave packet is spreading subdiffusively beyond the bounds set by $\xi_1$ and saturates at a new length scale $\xi_2 \gg \xi_1$. In particular we find $\xi_2 \sim \xi_1^{1.2}$ for $\gamma=\pi$. We observe a nontrivial dependence of $\xi_2$ on $\gamma$, with a maximum value observed for $\gamma$-values which are shifted away from the expected strongest interaction case $\gamma=\pi$. The novel Anderson localization regime violates single parameter scaling for both interacting and noninteracting walks.

cond-mat.dis-nn↗

arXiv2016

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 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 frequency corresponding to dispersion relation of the system. Amplification scenario happens when a counter phase pulse of 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 presented conceptual idea. Logical operations is the other probable field, where such mechanism could be used, which might significantly broaden the horizon of considered applications of band-gap soliton dynamics.

nlin.PS↗

arXiv2015

All-phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in Anharmonic Oscillator Ladder

A conceptual mechanism of amplification of phonons by phonons on the basis of 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 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 counter phase and with the same frequency as first chain. If the total driving of both chains overcomes the band-gap transmission threshold the large amplitude band-gap soliton emerges and amplification scenario is realized. The mechanism is interpreted as nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or band-pass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and has all the promises for logic gate operations.

nlin.PS↗