Exact versus tight-binding models in longitudinally modulated $\mathcal{PT}$-symmetric coupled waveguides

• URL: http://arxiv.org/abs/2605.23853v1
• Date: Fri, 22 May 2026 17:07:57 GMT
• Title: Exact versus tight-binding models in longitudinally modulated $\mathcal{PT}$-symmetric coupled waveguides
• Abstract summary: The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays.<n>Despite its success, its validity in $mathcalPT$-symmetric systems characterized by strong longitudinal modulation has not been rigorously benchmarked against exact analytical solutions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays. Despite its success, its validity in $\mathcal{PT}$-symmetric systems characterized by strong longitudinal modulation has not been rigorously benchmarked against exact analytical solutions. In this work, we address this gap by performing a comparative analysis between exact continuous solutions derived from $z$-dependent supersymmetric (SUSY) transformations and their corresponding discrete TB approximations. To achieve this, we develop a theoretical model for two PT-symmetric coupled waveguides subject to longitudinal modulation. We then evaluate the performance of the TB framework against the exact SUSY benchmark. Our results delineate the specific validity range of the TB approximation, demonstrating its proficiency in reproducing spatial intensity distributions. However, we also identify its limitations in accurately capturing the complex oscillatory phase dynamics inherent to this non-Hermitian evolution.

Related papers

• Deep Skew-t Mixture Models [2.5794915063815664]
  High-dimensional clustering is challenging when component distributions are both heavy-tailed and directionally asymmetric.<n>We propose a hierarchical factor-analytic mixture based on the generalised-hyperbolic skew-$t$ normal mean--variance representation.<n>A shared inverse-gamma mixing variable is propagated along each complete latent pathway, allowing heavy tails and directional asymmetry to be modelled jointly.
  arXiv  Detail & Related papers  (2026-09-01T06:02:11Z)
• Representation-Induced Symmetry Trapping in Adaptive Variational Quantum Simulations of Multi-Reference Topologies [0.0]
  We evaluate a spin-conserved SUSD operator pool across highly stretched configurations.<n>We show that the preservation of point-group symmetry structurally protects the optimization landscape.<n> exploiting structural overlap within our pool, we introduce a co-variance-driven, adaptive shot-allocation filter.
  arXiv  Detail & Related papers  (2026-06-11T14:16:11Z)
• Preventing the Breakdown of Tight-Binding Waveguide Optics by Löwdin Orthogonalization [0.0]
  We study the dynamics of the total light field by examining the coupling between the guided modes of individual single-mode substructures.<n>We introduce a modified TB framework based on the Lwdin orthogonalization, which constructs an orthonormal basis from the non-orthogonal guided modes.<n>The resulting Lwdin-TB method restores the standard eigenvalue problem and yields excellent agreement with exact beam propagation simulations.
  arXiv  Detail & Related papers  (2026-05-29T09:43:07Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Topological Residual Asymmetry for Bivariate Causal Direction [1.2691047660244335]
  Topological Residual Asymmetry is a geometry-based criterion for additive-noise models.<n>We quantify a bulk-tube contrast using a 0D persistent-homology functional.<n>Experiments across many challenging synthetic and real-data scenarios demonstrate the method's superiority.
  arXiv  Detail & Related papers  (2026-01-31T00:38:53Z)
• The Procrustean Bed of Time Series: The Optimization Bias of Point-wise Loss [53.542743390809356]
  This paper aims to provide a first-principles analysis of the Expectation of Optimization Bias (EOB)<n>Our analysis reveals a fundamental paradigm paradox: the more deterministic and structured the time series, the more severe the bias by point-wise loss function.<n>We present a concrete solution that simultaneously achieves both principles via DFT or DWT.
  arXiv  Detail & Related papers  (2025-12-21T06:08:22Z)
• Revisiting Zeroth-Order Optimization: Minimum-Variance Two-Point Estimators and Directionally Aligned Perturbations [57.179679246370114]
  We identify the distribution of random perturbations that minimizes the estimator's variance as the perturbation stepsize tends to zero.<n>Our findings reveal that such desired perturbations can align directionally with the true gradient, instead of maintaining a fixed length.
  arXiv  Detail & Related papers  (2025-10-22T19:06:39Z)
• Parametric resonant enhancement of motional entanglement under optimal control: an analytical study [45.88028371034407]
  We study theoretically continuous-variable entanglement between the motional degrees of freedom of optically trapped massive particles coupled via the Coulomb interaction.<n>We perform a detailed analysis of the parametric resonance induced by temporal modulation of the coupling strength, based on the system's coupled nonlinear, nonhomogeneous dynamical equations.<n>We demonstrate that a stationary nonequilibrium entangled state is realized as a result of the competition between parametric gain and decoherence.
  arXiv  Detail & Related papers  (2025-10-21T09:01:19Z)
• Exact Dynamics and Bloch Oscillations in a Non Hermitian Zigzag Glauber Fock Lattice [0.0]
  discrete dynamics of a one-dimensional non-hermitian waveguide array is studied theoretically.<n>The interplay between the unbalanced hopping amplitudes and the waveguide setup results in Non-Hermitian Bloch oscillations.<n>We derive a closed-form analytic solution, which is then compared with the numerical solution of the system.
  arXiv  Detail & Related papers  (2025-04-02T19:41:53Z)
• 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.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>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)
• Exact Floquet solutions in a Parity-Time-Symmetric Rabi Model [0.0]
  It is shown that a semiclassical Rabi model with parity-time (PT) symmetry has a hidden $sl(2)$ symmetry and hence possesses quasi-exact solutions.<n>The corresponding constraints on the model parameters can be interpreted as a resonance relationship between the constant and periodic driving terms.
  arXiv  Detail & Related papers  (2025-01-31T14:30:41Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)

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.