Energy transport and chaos in a one-dimensional disordered nonlinear stub lattice

TL;DR

This study explores how energy propagates and chaos develops in a disordered nonlinear stub lattice, revealing regimes of subdiffusive spreading and the impact of disorder on spectral gaps and dynamical behavior.

Contribution

It demonstrates the dynamical regimes of energy transport in a disordered nonlinear stub lattice and compares these to known models, extending understanding to flat-band network geometries.

Findings

Subdiffusive spreading observed with specific scaling laws.

Disorder fills spectral gaps, affecting energy transport.

Chaotic behavior decays over time with identifiable power laws.

Abstract

We investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, we show that sufficiently strong disorder fills all intermediate band gaps. By mapping the two-dimensional parameter space of disorder and nonlinearity, we identify three distinct dynamical regimes (weak chaos, strong chaos, and self-trapping) through numerical simulations of initially localized wave packets. When disorder is strong enough to close the frequency gaps, the results closely resemble those obtained in the one-dimensional disordered discrete nonlinear Schr\"{o}dinger equation and Klein-Gordon lattice model. In particular, subdiffusive spreading is observed in both the weak and strong chaos regimes, with the second moment $m_2$ of the norm distribution scaling as $m_2 \propto t^{0.33}$ and $m_2 \propto t^{0.5}$, respectively. The system's chaotic behavior follows a similar trend, with the finite-time maximum Lyapunov exponent $\Lambda$ decaying as $\Lambda \propto t^{-0.25}$ and $\Lambda \propto t^{-0.3}$. For moderate disorder strengths, i.e., near the point of gap closing, we find that the presence of small frequency gaps does not exert any noticeable influence on the spreading behavior. Our findings extend the characterization of nonlinear disordered lattices in both weak and strong chaos regimes to other network geometries, such as the stub lattice, which serves as a representative flat-band system.