Resonant Weighted Nonlocal Schrödinger Equation with Gauge Invariance, Conservation Laws and Measurable Phase Detuning
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2025
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| author | Yildiz, L. Kayki, D. Gudekli, E. |
| author_facet | Yildiz, L. Kayki, D. Gudekli, E. |
| contents | We present a gauge-invariant Schrödinger-type evolution that combines (i) weighted local diffusion, (ii) symmetric nonlocal exchange through a kernel operator, and (iii) a mean-free phase-resonant drive. The resulting Resonant Weighted Nonlocal Schrödinger (RWNS) equation exactly conserves mass and, when the drive is absent, admits a Hamiltonian structure with energy conservation. Under standard assumptions on the weight, kernel, and nonlinearity, we establish local well-posedness in $H^1$ and provide defocusing conditions for global continuation. Linearization yields a dispersion relation in which the nonlocal kernel and the mean-free phase field contribute additively to a measurable spectral detuning. Building on this, we define two observables: a wavenumber-resolved detuning $Δω(k)$ and a kernel-contrast functional $Ξ[ψ]$ that isolates the nonlocal exchange. We outline feasible implementations in nonlinear-optical lattices and cavity-assisted cold-atom platforms, and discuss conceptual links to propagation-induced phase signatures in astrophysical media. The RWNS model thus offers a compact and analytically tractable framework that unifies weighted local dynamics, symmetric nonlocality, and a mean-free phase drive, yielding clear, testable predictions for laboratory measurements and, in principle, precision timing data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_18887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resonant Weighted Nonlocal Schrödinger Equation with Gauge Invariance, Conservation Laws and Measurable Phase Detuning Yildiz, L. Kayki, D. Gudekli, E. Mathematical Physics We present a gauge-invariant Schrödinger-type evolution that combines (i) weighted local diffusion, (ii) symmetric nonlocal exchange through a kernel operator, and (iii) a mean-free phase-resonant drive. The resulting Resonant Weighted Nonlocal Schrödinger (RWNS) equation exactly conserves mass and, when the drive is absent, admits a Hamiltonian structure with energy conservation. Under standard assumptions on the weight, kernel, and nonlinearity, we establish local well-posedness in $H^1$ and provide defocusing conditions for global continuation. Linearization yields a dispersion relation in which the nonlocal kernel and the mean-free phase field contribute additively to a measurable spectral detuning. Building on this, we define two observables: a wavenumber-resolved detuning $Δω(k)$ and a kernel-contrast functional $Ξ[ψ]$ that isolates the nonlocal exchange. We outline feasible implementations in nonlinear-optical lattices and cavity-assisted cold-atom platforms, and discuss conceptual links to propagation-induced phase signatures in astrophysical media. The RWNS model thus offers a compact and analytically tractable framework that unifies weighted local dynamics, symmetric nonlocality, and a mean-free phase drive, yielding clear, testable predictions for laboratory measurements and, in principle, precision timing data. |
| title | Resonant Weighted Nonlocal Schrödinger Equation with Gauge Invariance, Conservation Laws and Measurable Phase Detuning |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2510.18887 |