Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling

• URL: http://arxiv.org/abs/2212.13765v2
• Date: Thu, 6 Jul 2023 14:30:59 GMT
• Title: Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling
• Authors: Hui Jiang, Enhong Cheng, Ziyu Zhou, and Li-Jun Lang
• Abstract summary: We study the nonlinear perturbation of a high-order exceptional point (EP) of the order equal to the system site number $L$ in a Hatano-Nelson model. We find a class of discrete breathers that aggregate to one boundary, here named as it skin discrete breathers (SDBs) The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.
• Score: 5.249388938927588
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the nonlinear perturbation of a high-order exceptional point (EP) of the order equal to the system site number $L$ in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity. Notably, We find a class of discrete breathers that aggregate to one boundary, here named as {\it skin discrete breathers} (SDBs). The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP. Specifically, the response of nonlinear energy to the perturbation is given by $E_m\propto \varGamma^{\alpha_{m}}$, where $\alpha_m=3^{m-1}$ is the power with $m=1,\cdots,L$ labeling the nonlinear energy bands. This is in sharp contrast to the $L$-th root of a linear perturbation in general. These SDBs decay in a double-exponential manner, unlike the edge states or skin modes in linear systems, which decay exponentially. Furthermore, these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity. They are also stable, as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis. As nonreciprocal nonlinear models may be experimentally realized in various platforms, such as the classical platform of optical waveguides, where Kerr nonlinearity is naturally present, and the quantum platform of optical lattices with Bose-Einstein condensates, our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity, particularly on high-order EPs, and benchmark the relevant simulations.

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)
• Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping [0.0]
  We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr"odinger equation in finite square lattices.<n>We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes.<n>We identify distinct self-trapped regimes characterized by diagonal or off-diagonal localized modes, depending on the strength of $U$.
  arXiv  Detail & Related papers  (2025-10-09T19:59:13Z)
• 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)
• 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. 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)
• Nonlinear Stochastic Gradient Descent and Heavy-tailed Noise: A Unified Framework and High-probability Guarantees [56.80920351680438]
  We study high-probability convergence in online learning, in the presence of heavy-tailed noise. Compared to state-of-the-art, who only consider clipping and require noise with bounded $p$-th moments, we provide guarantees for a broad class of nonlinearities.
  arXiv  Detail & Related papers  (2024-10-17T18:25:28Z)
• Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-Lévy-index fractional Kerr media [13.082347639610987]
  Modulation instability of continuous waves is investigated in the two-L'evy-index system too. We produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.
  arXiv  Detail & Related papers  (2024-09-02T10:16:53Z)
• Continuous-Wave Nonlinear Polarization Control and Signatures of Criticality in a Perovskite Cavity [0.0]
  We demonstrate continuous-wave (CW) nonlinearities in a CsPbBr$_3$ perovskite cavity. We exploit the interplay of nonlinearity and birefringence to demonstrate nonlinear control over the polarization light. Our results position CsPbBr$_3$ as an exceptional platform for nonlinear optics, offering strong CW nonlinearity and birefringence.
  arXiv  Detail & Related papers  (2024-07-08T12:05:09Z)
• Josephson bifurcation readout: beyond the monochromatic approximation [49.1574468325115]
  We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits. This circuit can serve as an efficient detector of the quantum state of superconducting qubits.
  arXiv  Detail & Related papers  (2024-05-25T22:22:37Z)
• Observation of the spectral bifurcation in the Fractional Nonlinear Schr\"{o}dinger Equation [6.4477590105028]
  We report a comprehensive investigation and experimental realization of spectral bifurcations of ultrafast soliton pulses. We propose an effective force' model based on the frequency chirp, which characterizes their interactions as either repulsion', attraction', or equilibration. The proposal for engineering spectral bifurcation patterns holds significant potential for ultrafast signal processing applications.
  arXiv  Detail & Related papers  (2023-11-26T00:34:15Z)
• High-probability Convergence Bounds for Nonlinear Stochastic Gradient Descent Under Heavy-tailed Noise [59.25598762373543]
  We show that wetailed high-prob convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. We demonstrate analytically and that $ta$ can be used to the preferred choice of setting for a given problem.
  arXiv  Detail & Related papers  (2023-10-28T18:53:41Z)
• 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)
• On the quantization of AB phase in nonlinear systems [3.515802569456161]
  We study the Aharonov-Bohm phase associated with an adiabatic process in the momentum space. For and only for Kerr nonlinearity, the AB phase experiences a jump of $pi$ at the critical nonlinearity. Our results may be useful for experimental measurement of power-law nonlinearity.
  arXiv  Detail & Related papers  (2022-12-05T08:02:17Z)
• Nonlinear flip-flop quantum walks through potential barriers [0.0]
  nonlinear flip-flop quantum walk with amplitude-dependent phase shifts with pertubing potential barrier is investigated. We show the existence of different Hadamard quantum walking regimes, including those with mobile soliton-like structures or self-trapped states.
  arXiv  Detail & Related papers  (2022-10-21T01:11:26Z)
• Fast quantum state discrimination with nonlinear PTP channels [0.0]
  We investigate models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and evolution equations. PTP channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states. We argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault-tolerant nonlinear state discriminator.
  arXiv  Detail & Related papers  (2021-11-10T22:42:37Z)
• Robust Online Control with Model Misspecification [96.23493624553998]
  We study online control of an unknown nonlinear dynamical system with model misspecification. Our study focuses on robustness, which measures how much deviation from the assumed linear approximation can be tolerated.
  arXiv  Detail & Related papers  (2021-07-16T07:04:35Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)

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.