线性 sigma 模型中旋转夸克物质的防火墙边界与混合相
Firewall boundaries and mixed phases of rotating quark matter in linear sigma model
AI总结：
本文在线性 sigma 模型中研究刚性旋转夸克物质，通过三类凝聚近似揭示非均匀性导致的 Tolman–Ehrenfest 偏离，并提出光锥防火墙边界条件与混合相图。
摘要：
无界空间中的刚性旋转体通常被认为是一种病态系统，因为它会导致超光速以及相关的因果性破坏。然而，关于相互作用费米子旋转等离子体中手征对称性破缺的数值结果揭示，严格的有界方法与形式上的无界方法在预测上存在令人惊讶的密切对应。为深入理解这种关联，我们考虑在无界 Minkowski 时空中经历刚性旋转的、与夸克耦合的线性 sigma 模型。在平均场方法内，我们对系统基态采用三个连续的近似层级，分别以均匀（模型 1）、弱非均匀（模型 2）和完全非均匀（模型 3）凝聚为特征。未考虑凝聚空间梯度的模型 1 和模型 2 与 Tolman–Ehrenfest 定律相符。模型 3 由于出现由基态非均匀性设定的新能量尺度，表现出对 Tolman–Ehrenfest 预测的偏离。其边界条件通过要求旋转轴处的正则性以及全局最小化巨势来确定。我们将后者称为“防火墙边界条件”，它转化为光锥上凝聚为零的要求，这源于系统状态在光锥上形式上发散的事实。在所有模型中，我们给出了系统的相图，并指出在模型 2 和模型 3 中，系统要么处于手征恢复相，要么处于具有空间分离的手征恢复相和手征破缺相的混合相。最后，我们使用 Rankine 涡旋模型的相对论版本讨论了系统在非均匀旋转下的性质。
英文摘要：
A rigidly-rotating body in unbounded space is usually considered a pathological system since it leads to faster-than-light velocities and associated breaches of causality. However, numerical results on chiral symmetry breaking in rotating plasmas of interacting fermions reveal surprisingly close correspondence in predictions between the rigorous bounded and formal unbounded approaches. To provide insight into this correlation, we consider the linear sigma model coupled to quarks, undergoing rigid rotation in unbounded Minkowski space-time. Within the mean-field approach, we adopt three consecutive levels of approximation to the ground state of the system that feature uniform (model 1), weakly inhomogeneous (model 2) and fully inhomogeneous (model 3) condensates. Models 1 and 2 that do not take into account spatial gradients of the condensate show agreement with the Tolman-Ehrenfest law. Model 3 exhibits a deviation from the Tolman-Ehrenfest prediction due to the appearance of a new energy scale set by the inhomogeneity of the ground state. Its boundary conditions are fixed by imposing regularity at the rotation axis and by demanding the global minimization of the grand potential. We dub the latter as ``firewall boundary conditions,'' translating into the requirement of vanishing condensate on the light cylinder, which follows from the fact that the system state formally diverges at the light cylinder. In all models, we present the phase diagram of the system and point out that in models 2 and 3, the system resides either in a chirally-restored phase, or in a mixed phase that possesses spatially-separated chirally-restored and chirally-broken phases. Finally, we discuss the properties of the system under inhomogeneous rotation using the relativistic version of the Rankine vortex model.
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