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

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Hauptverfasser: Cheong, Su Ho, Ngapasare, Arnold, Achilleos, Vassos, Theocharis, Georgios, Richoux, Olivier, Skokos, Charalampos
Format: Preprint
Veröffentlicht: 2025
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author Cheong, Su Ho
Ngapasare, Arnold
Achilleos, Vassos
Theocharis, Georgios
Richoux, Olivier
Skokos, Charalampos
author_facet Cheong, Su Ho
Ngapasare, Arnold
Achilleos, Vassos
Theocharis, Georgios
Richoux, Olivier
Skokos, Charalampos
contents 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 Schrödinger 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 $Λ$ decaying as $Λ\propto t^{-0.25}$ and $Λ\propto t^{-0.3}$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_04159
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Energy transport and chaos in a one-dimensional disordered nonlinear stub lattice
Cheong, Su Ho
Ngapasare, Arnold
Achilleos, Vassos
Theocharis, Georgios
Richoux, Olivier
Skokos, Charalampos
Chaotic Dynamics
Disordered Systems and Neural Networks
Statistical Mechanics
Dynamical Systems
Computational Physics
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 Schrödinger 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 $Λ$ decaying as $Λ\propto t^{-0.25}$ and $Λ\propto t^{-0.3}$. 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.
title Energy transport and chaos in a one-dimensional disordered nonlinear stub lattice
topic Chaotic Dynamics
Disordered Systems and Neural Networks
Statistical Mechanics
Dynamical Systems
Computational Physics
url https://arxiv.org/abs/2511.04159