Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials

• URL: http://arxiv.org/abs/2309.16904v1
• Date: Fri, 29 Sep 2023 00:10:25 GMT
• Title: Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials
• Authors: Jin Song, Boris A. Malomed, Zhenya Yan
• Abstract summary: We address symmetry breaking bifurcations (SBBs) in the ground-state (GS) and dipole-mode (DM) solitons of the 1D linearly coupled NLS equations. A novel feature of the system is interplay between breakings of the PT and inter-core symmetries.
• Score: 0.3683202928838613
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address symmetry breaking bifurcations (SBBs) in the ground-state (GS) and dipole-mode (DM) solitons of the 1D linearly coupled NLS equations, modeling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of PT-symmetric potentials. The PT-symmetric potential is employed to obtained different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the PT and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of PT-symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the PT symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential's parameters or the system's coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with PT potential and related experimental designs.

Related papers

• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model [32.553027955412986]
  We investigate the anisotropic coupled-top model, which describes the interactions between two large spins along both $x-$ and $y-$directions. We can manipulate the system's symmetry, inducing either discrete $Z$ or continuous U(1) symmetry. The framework provides an ideal platform for experimentally controlling symmetries and investigating associated physical phenomena.
  arXiv  Detail & Related papers  (2025-02-13T15:14:29Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency. We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Beyond the Permutation Symmetry of Transformers: The Role of Rotation for Model Fusion [43.299430093251736]
  We introduce rotation symmetry, a novel form of parameter space symmetry for transformers. Unlike permutation symmetry, rotation symmetry operates in a continuous domain, thereby significantly expanding the equivalence set for transformers. We propose a theoretically optimal matching algorithm as a plug-and-play module to enhance model fusion.
  arXiv  Detail & Related papers  (2025-02-01T01:44:55Z)
• Eigenmodes of latent-symmetric quantum photonic networks [37.69303106863453]
  We study the eigenmodes of a 9-site latent-symmetric photonic network. Latent symmetries introduce a powerful new set of tools to the design of systems with desired functionality on any nanophotonic platform.
  arXiv  Detail & Related papers  (2025-01-22T17:21:21Z)
• 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)
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• Latent Space Symmetry Discovery [31.28537696897416]
  We propose a novel generative model, Latent LieGAN, which can discover symmetries of nonlinear group actions. We show that our model can express nonlinear symmetries under some conditions about the group action. LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
  arXiv  Detail & Related papers  (2023-09-29T19:33:01Z)
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schr\"odinger equation with focusing saturable nonlinearity and PT-symmetric potential [13.844860643212105]
  We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schr"odinger (FNLS) equation. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. We explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons.
  arXiv  Detail & Related papers  (2022-10-01T13:18:22Z)
• Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schr\"odinger equations [2.8331714502894396]
  PT-symmetric generalized Scarf-II (GS-II) potentials can support exact solitons in one- and multi-dimensional nonlinear Schr"odinger equation. continuous families of fundamental and higher-order solitons are produced. stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells.
  arXiv  Detail & Related papers  (2021-11-18T02:25:52Z)
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems [0.0]
  The symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The odd-parity symmetries including the particle-hole symmetry, chiral symmetry, and sublattice symmetry cannot ensure the scattering to be symmetric. Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.
  arXiv  Detail & Related papers  (2021-01-04T10:30:00Z)
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models [0.0]
  The asymmetric quantum Rabi model (AQRM) has a broken $mathbbZ$ symmetry, with generally a non-degenerate eigenvalue spectrum. This unknown "symmetry" has thus been referred to as hidden symmetry in the literature. We show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term.
  arXiv  Detail & Related papers  (2020-07-13T11:06:52Z)

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.