In this paper, we examine the time-fractional Schrödinger equation from the perspective of non-Markovian dynamics in dissipative systems. First, we determine the range of the fractional derivative’s order by examining the memory properties of the time-fractional Schrödinger equation. Next, we employ the Jaynes–Cummings model to identify the appropriate mathematical form of the imaginary unit. Finally, we use the refined equation to study quantum teleportation under amplitude damping noise. It was found that the time-fractional Schrödinger equation without fractional operations on the imaginary unit i might be more suitable for describing non-Markovian dynamics in dissipative systems. Our research may provide a new perspective on the time-fractional Schrödinger equation, contributing to a deeper understanding and further development of time-fractional quantum mechanics.

This paper develops a physically consistent precoding framework for extremely large antenna arrays (ELAAs), incorporating structural mutual coupling through a two-dimensional impedance network. To maintain scalability, we introduce a Neumann series approximation for the inverse coupling operator. Our analysis reveals that coupling-aware received power maximization reduces to a Hermitian rank-one quadratic form, whose optimum aligns with the dominant eigendirection of the effective coupling-shaped channel. This result indicates that both eigen-decomposition-based optimization and coupling-aware maximum ratio transmission (MRT) enhance power efficiency under mutual coupling, with the eigenmode design achieving superior performance. In addition, we further extend the analysis from the free-space path to the multipath scenario, demonstrating the robustness and adaptability of the proposed method under practical propagation conditions. Simulations confirm that structural coupling severely degrades conventional MRT, whereas the proposed eigenmode method with Neumann approximated coupling attains the highest received power among all considered schemes. The framework is interpretable, numerically stable, and readily implementable, offering practical guidance for energy-efficient near-field beamforming on ultra-large apertures.

In this paper, we investigate the memory effects introduced by the time-fractional Schrödinger equation proposed by Naber on quantum entanglement and quantum dense coding under amplitude damping noise. Two formulations are analyzed: one with fractional operations applied to the imaginary unit and one without. Numerical results show that the formulation without fractional operations on the imaginary unit may be more suitable for describing non-Markovian (power-law) behavior in dissipative environments. This finding provides a more physically meaningful interpretation of the memory effects in time-fractional quantum dynamics and indirectly addresses fundamental concerns regarding the violation of unitarity and probability conservation in such frameworks. Our work offers a new perspective for the application of fractional quantum mechanics to realistic open quantum systems and shows promise in supporting the theoretical modeling of decoherence and information degradation.

Hybrid deep learning frameworks integrating convolutional neural networks (CNNs) and Transformer-based attention mechanisms have recently achieved promising results in synthetic aperture radar (SAR) ship detection. However, they still suffer from inherent limitations, including missed detections of small-scale ships under large variations in target scales, multiplicative speckle noise, and complex sea clutter interference. To address these issues, this paper proposes ACmixSAR-YOLO11, a SAR ship detection framework built upon YOLO11. The proposed model incorporates three complementary improvements to enhance feature representation and multi-scale detection capability. First, an ACmixSAR module is designed by integrating convolutional operations with self-attention mechanisms. This design strengthens feature discriminability. Second, a SARNoiseGate gating mechanism is embedded into the ACmixSAR module, which is designed to suppress low signal-to-noise ratio (SNR) feature responses while preserving discriminative ship features. Third, we develop a scale-weighted complete intersection over union (SW-CIoU) loss function, which assigns adaptive regression weights based on target sizes to rebalance the optimization across small, medium, and large ships. All improvements below are reported as relative percentage changes. Experimental results on the SSDD dataset demonstrate that the proposed ACmixSAR-YOLO11 outperforms the original YOLO11 Baseline, achieving a 1.50% increase in precision, a 0.15% growth in recall, a 1.47% enhancement in mAP@0.5, and a 4.26% promotion in mAP@0.5:0.95. Significance testing was applied to mAP@0.5 only (paired one-sided t-test, p = 0.0058 < 0.01); the other three metrics are reported as three-seed means and spreads. As supplementary evidence, experiments on HRSID show improved recall, mAP@0.5 and mAP@0.5:0.95 under conventional patch-level splitting at the cost of slightly reduced precision. However, this patch-level performance gain is partially inflated by scene overlap between training and test patches. Further validation on a strictly leakage-free scene-level split of HRSID shows that the overall mAP@0.5 gain diminishes to within random seed fluctuation, while improvements in mAP@0.5:0.95 and precision remain observable. These results demonstrate that the proposed framework effectively enhances detection accuracy with a moderate parameter increase (9.69 M → 11.75 M) while maintaining real-time inference.

Object detection in complex underwater environments remains challenging due to low contrast, light scattering, noise interference, and indistinct texture and boundary information of small objects. To improve the representation capability for small objects, weak-texture objects, and objects with blurred boundaries, this study proposes an improved underwater object detection model, SFL-YOLO, based on YOLOv11n. First, a Spatial Channel Transform Convolution module (SCTC) is designed to replace conventional strided downsampling. By integrating spatial-channel rearrangement, local detail response, and detail selection gating, SCTC preserves more edge, texture, and contour information while reducing the feature map resolution. Second, a Feature-Aware Reassembly Upsampling module (FARU) is introduced. By combining content-aware reassembly, local detail guidance, and degradation-aware modulation, FARU alleviates semantic misalignment and background noise diffusion caused by fixed-interpolation upsampling. Finally, a Lightweight Detail Modeling Detection Head (LDMDH) is proposed to enhance fine-grained feature representation in the detection head while reducing parameter redundancy. Experimental results show that SFL-YOLO achieves 85.4% mAP@0.5 on the URPC2020 dataset, improving YOLOv11n by 1.6% points. The model has 4.50 M parameters and 11.4G FLOPs, with a complete inference speed of 142 FPS. On the RUOD dataset, SFL-YOLO achieves 85.7% mAP@0.5, outperforming YOLOv11n by 1.1% points. Ablation experiments and controlled degradation experiments further verify the effectiveness of each module and the robustness of the model on degraded underwater images. These results demonstrate that SFL-YOLO improves object detection accuracy in complex underwater environments while maintaining real-time performance.