标题： DSR中的狄拉克振子：马格伊奥-斯莫林模型与阿梅利诺-卡梅利亚模型的比较研究 显示英文标题

标题： Dirac Oscillator in DSR: A Comparative Study of Magueijo-Smolin and Amelino-Camelia Models

摘要： 本文研究了在双重特殊相对论（DSR）框架下的狄拉克振子的能量谱，重点研究了两个显著模型：Magueijo--Smolin（MS）和Amelino-Camelia模型。 我们在单个粒子的$$O(E^{2}/k^{2})$$近似下，推导了MS和Amelino-Camelia DSR模型中的修正狄拉克方程，并研究了由此产生的能量谱。 研究表明，由于普朗克尺度变形参数$$k$$的存在，标准相对论狄拉克振子谱出现了显著修正，这会根据所采用的DSR模型引入不同的偏差。 对于MS模型，在小$$k$$时，正负能分支出现非均匀位移，随着$$k$$的增加，谱逐渐趋近于规范结果。 在Amelino-Camelia模型中，能量级在$$k$$较低时表现出更大的偏差，且这些异常比MS模型减小得更慢。 结果为量子引力效应对量子系统的影响提供了见解，可能在接近普朗克尺度的能量下的高精度光谱或天体物理观测中有应用。 此外，对这两个DSR模型的比较分析突显了普朗克尺度预测的稳健性，并指导了未来旨在探测量子引力特征的实验工作。 显示英文摘要

摘要： This paper investigates the energy spectrum of the Dirac oscillator within the framework of Doubly Special Relativity (DSR), focusing on two prominent models: the Magueijo--Smolin (MS) and Amelino-Camelia models. We derive the modified Dirac equations in both MS and Amelino-Camelia DSR models under the approximation of $$O(E^{2}/k^{2})$$ for a single particle and examine the resulting energy spectra. The study reveals significant corrections to the standard relativistic Dirac oscillator spectrum due to the Planck-scale deformation parameter $$k$$, which introduces distinct deviations depending on the DSR model employed. For the MS model, we observe non-uniform shifts in both positive and negative energy branches at small $$k$$, with the spectrum gradually flattening toward the canonical result as $$k$$ increases. In the Amelino-Camelia model, the energy levels show larger deviations at lower values of $$k$$, and these anomalies diminish more slowly compared to the MS model. The results provide insights into the impact of quantum gravity effects on quantum systems, with potential applications in high-precision spectroscopic or astrophysical observations at energies near the Planck scale. Furthermore, the comparative analysis of these two DSR models highlights the robustness of Planck-scale predictions and guides future experimental efforts aimed at detecting quantum-gravity signatures.