Nonlinearity-Induced Thouless Pumping in Quasiperiodic Lattices

• URL: http://arxiv.org/abs/2604.00639v1
• Date: Wed, 01 Apr 2026 08:45:30 GMT
• Title: Nonlinearity-Induced Thouless Pumping in Quasiperiodic Lattices
• Abstract summary: We show a nonlinear topological pumping of gap solitons in quasiperiodic lattices where the local nonlinear self-consistent potentials lead to a lattice potential reconstruction.<n>Our work uncovers a mechanism for nonlinearity-induced topological behavior in complex lattice potentials.
• Score: 2.8814760192686983
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Nonlinear Thouless pumping has been established in periodic lattices; its counterpart in quasiperiodic lattices remains unexplored. Here, we show a nonlinear topological pumping of gap solitons in quasiperiodic lattices where the local nonlinear self-consistent potentials lead to a lattice potential reconstruction; as a result, an emergent topological structure induced by this local reconstruction governs the dynamics of the gap solitons. This enables solitons to adiabatically occupy a single topological band, realizing quasi-quantized Thouless pumping. In addition, the intrinsic lattice perturbations disrupt this band occupation, which drives solitons into a non-quantized drifting regime. However, even in this regime, we also find that the soliton transport is constrained by the topological properties of a critical rational approximant. Tuning nonlinearity or lattice scaling reveals a controllable switching among topological pumping, drifting, and localization. Our work uncovers a mechanism for nonlinearity-induced topological behavior in complex lattice potentials.

Related papers

• Topological States Enabled by Non-local Nonlinearity in Synthetic Dimensions [0.0]
  We consider a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions.<n>We find that the distinctive nonlinearity maintains an effective chiral symmetry and leads to a quantized nonlinear winding and Berry phase.<n>Our results establish a rigorous framework and pave the way for exploring nonlinear topological phenomena.
  arXiv  Detail & Related papers  (2026-01-05T15:23:55Z)
• Cusp solitons mediated by a topological nonlinearity [0.0]
  We introduce a nonlinear Schr"odinger model whose dynamics are dependent on the curvature of the wavefunction intensity and show that this has a direct link to a topological quantity from persistent homology.<n>Our model energetically penalizes or favours the formation of local extrema and we demonstrate through numerical simulations that this topological nonlinearity leads to the emergence of robust, cusp-like soliton structures.<n>These findings suggest that topological nonlinearities could serve as a versatile tool for controlling nonlinear waves in optics and Bose-Einstein condensates.
  arXiv  Detail & Related papers  (2025-09-23T04:15:48Z)
• Quantized nonlinear kink movement through topological boundary state instabilities [0.0]
  We study a nonlinear dimer-chain model that exhibits quantized transport of kinks under a periodic modulation of a pumping parameter.<n>We show that instabilities in these boundary modes are the driving mechanism behind the observed kink motion.<n>Our results unify concepts from linear topology and nonlinear dynamics to establish a framework for quantized transport in nonlinear media.
  arXiv  Detail & Related papers  (2025-08-16T16:46:19Z)
• Topological Invariants in Nonlinear Thouless Pumping of Solitons [8.026610383567432]
  We introduce a unified topological invariant applicable across both weakly and strongly nonlinear regimes.<n>In the weak nonlinearity regime, where the nonlinear bands are wellseparated, the invariant reduces to the Abelian Chern number of the occupied nonlinear band.<n>As the nonlinearity increases, the nonlinear bands start to intertwine, leading to a situation where the invariant is expressed as the non-Abelian Chern number divided by the number of interacting bands.
  arXiv  Detail & Related papers  (2025-06-10T06:58:15Z)
• Non-Hermitian topology and skin modes in the continuum via parametric processes [44.99833362998488]
  We show that Hermitian, nonlocal parametric pairing processes can induce non-Hermitian topology and skin modes.<n>Our model, stabilized by local dissipation, reveals exceptional points that spawn a tilted diabolical line in the dispersion.
  arXiv  Detail & Related papers  (2025-05-05T16:38:20Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking [79.16635054977068]
  We consider a chain of parametrically-driven quantum resonators coupled only via weak nearest-neighbour cross-Kerr interaction.<n>Topology is dictated by the structure of the Kerr nonlinearity, yielding a non-trivial bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2025-03-15T00:20:45Z)
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics.<n>We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Dynamical chaos in nonlinear Schr\"odinger models with subquadratic power nonlinearity [137.6408511310322]
  We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity. We show that the spreading process is subdiffusive and has complex microscopic organization. The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
  arXiv  Detail & Related papers  (2023-01-20T16:45:36Z)
• Breakdown of quantization in nonlinear Thouless pumping [0.0]
  This work uncovers the fate of nonlinear Thouless pumping in the regime of intermediate nonlinearity. We identify the presence of critical nonlinearity strength at which quantized pumping of solitons breaks down regardless of the protocol time scale.
  arXiv  Detail & Related papers  (2022-05-23T01:06:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.