论文标题
与自旋的相对论流体中的量子流体对应：从Madelung形式到重力耦合
Quantum-Fluid Correspondence in Relativistic Fluids with Spin: From Madelung Form to Gravitational Coupling
论文作者
论文摘要
本文探讨了带有内在自旋的带电相对论流体中的量子流体对应关系。我们首先检查了非依赖主义情况，表明旋转的包含引入了对经典流体能量的量子校正。这种校正与麦克斯韦方程式相结合，自然会导致以马德隆形式的schrödinger方程。在这个基础的基础上，我们将形式主义扩展到相对论的完美液体，从而识别系统的应力能量量张量。我们的分析表明，对该张量的量子校正的痕迹对应于振荡器的能量密度，其频率取决于自旋运动的涡度。然后，我们使用应力 - 能量量张量来建立RICCI标量曲率之间的关系，如爱因斯坦磁场方程所规定，并且在静态的，球面上对称的构型中的流体密度。最后，我们通过开发量身定制的Clebsch表示速度场的量身定制的Clebsch表示，将Madelung转换概括为可压缩的Navier-Stokes流动。该理论框架为研究具有内部旋转自由度的流体样系统提供了潜在的应用，通常在天体物理环境中遇到。
This paper explores the quantum-fluid correspondence in a charged relativistic fluid with intrinsic spin. We begin by examining the nonrelativistic case, showing that the inclusion of spin introduces a quantum correction to the classical fluid energy. This correction, coupled with Maxwell's equations, naturally leads to the Schrödinger equation in Madelung form. Building on this foundation, we extend the formalism to a relativistic perfect fluid, identifying the system's stress-energy-momentum tensor. Our analysis reveals that the trace of the quantum correction to this tensor corresponds to the energy density of an oscillator, with its frequency determined by the vorticity of the spin motion. We then use the stress-energy-momentum tensor to establish the relationship between the Ricci scalar curvature, as dictated by the Einstein field equations, and the fluid density in a static, spherically symmetric configuration. Lastly, we generalize the Madelung transformation to compressible Navier-Stokes flows with vorticity and viscosity by developing a tailored Clebsch representation of the velocity field. This theoretical framework offers potential applications for studying fluid-like systems with internal rotational degrees of freedom, commonly encountered in astrophysical settings.
