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arXiv 2603.07553gr-qc
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缓慢旋转时空中的约瑟夫森效应

Josephson Effects in Slowly Rotating Spacetimes

Namangan State University(纳曼干国立大学);Mapúa University(马普阿大学);Eastern Mediterranean University(东地中海大学);Institute for Advanced Studies, New Uzbekistan University(新乌兹别克斯坦大学高级研究所);National University of Uzbekistan(乌兹别克斯坦国立大学);Harbin Institute of Technology(哈尔滨工业大学);Tashkent State Technical University(塔什干国立技术大学);University of Tashkent for Applied Sciences(塔什干应用科学大学)

Nurmukhammed Aytimbetov, Reggie C. Pantig, Ali Övgün, Bobomurat Ahmedov, Javlon Rayimbaev

AI总结:

研究缓慢旋转时空中的约瑟夫森效应,分析引力红移与旋转框架拖拽的影响,揭示约瑟夫森效应在不同坐标系下的表现及旋转对临界电流的影响。

摘要:

我们研究了缓慢旋转静态时空中的约瑟夫森现象,强调了引力红移和旋转框架拖拽的不同作用,受[10.1007/JHEP02(2026)006]的启发。基于协变公式,基于规范不变的相动力学和守恒电流,在$3+1$分解中,我们分析了AC和DC约瑟夫森效应和干涉配置。限制在旋转参数$a$的一阶范围内,并在欧拉ian/ZAMO框架中,我们显示在本文采用的缓慢旋转切片中,lapse函数与静态(Schwarzschild型)形式在$\mathcal{O}(a^2)$范围内一致,而旋转效应通过位移向量进入。因此,在$\mathcal{O}(a)$范围内,约瑟夫森频率和DC临界电流的红移效应相对于非旋转情况保持不变。AC约瑟夫森关系在用适当电压表达时保留其红移结构,当用渐近(Killing时间)可观测量表达时,其形式恢复为标准平坦时空形式。同样,无限远处测量的DC临界电流与lapse函数的单次幂成正比,并在无 azimuthal 超流体动量的情况下不受旋转影响。旋转效应只有在对空间相传输或与全局时间坐标同步敏感的配置中才相关。特别是,RF驱动的干涉配置可以获取与框架拖拽相关的Sagnac型相偏移,而DC磁通量约束在当前近似下在$\mathcal{O}(a)$范围内保持不变。我们的结果为约瑟夫森物理中的lapse驱动红移效应和shift驱动旋转贡献提供了清晰的分离,并为静态时空中的超导电路提供了一致的框架。

英文摘要:

We investigate Josephson phenomena in a slowly rotating stationary spacetime, emphasizing the distinct roles of gravitational redshift and rotational frame dragging motivated by [10.1007/JHEP02(2026)006]. Using a covariant formulation based on gauge-invariant phase dynamics and conserved currents within a $3+1$ decomposition, we analyze both AC and DC Josephson effects and interferometric configurations. Restricting attention to linear order in the rotation parameter $a$, and working in the Eulerian/ZAMO frame, we show that in the slow-rotation slicing adopted here the lapse function agrees with its static (Schwarzschild-type) form up to $\mathcal{O}(a^2)$, while rotational effects enter through the shift vector. Consequently, redshift effects on Josephson frequencies and DC critical currents remain unchanged relative to the non-rotating case at $\mathcal{O}(a)$. The AC Josephson relation retains its redshifted structure when expressed in terms of proper voltages and reduces to the standard flat-spacetime form when formulated in terms of asymptotic (Killing-time) observables. Likewise, the DC critical current measured at infinity scales with a single power of the lapse function and is unaffected by rotation at linear order in the absence of azimuthal condensate momentum. Rotational effects become relevant only in configurations sensitive to spatial phase transport or to synchronization with respect to the global time coordinate. In particular, RF-driven interferometric setups can acquire Sagnac-type phase offsets associated with frame dragging, whereas the DC fluxoid constraint remains unshifted at linear order in the present approximation. Our results provide a clean separation between lapse-driven redshift effects and shift-driven rotational contributions in Josephson physics and furnish a consistent framework for superconducting circuits in stationary spacetimes.

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