刚性旋转下相对论性玻色气体的热力学性质
Thermodynamic properties of a relativistic Bose gas under rigid rotation
AI总结：
本文研究刚性旋转相对论性玻色气体的热力学性质，利用Fock-Schwinger方法推导传播子并计算热力学势，发现高温大耦合下出现转动惯量为零导致的超涡旋现象及超光速声速等热力学不稳定性。
摘要：
我们研究了刚性旋转的相对论性玻色气体的热力学性质。首先，我们推导了与旋转复克莱因-戈尔登场对应的运动方程的解，并利用Fock-Schwinger固有时方法确定了该模型的自由传播子。利用该传播子，我们随后得到了该模型在零阶和一阶微扰水平下的热力学势。此外，我们还计算了该势的非微扰环贡献。我们重点关注这些表达式对角速度的依赖关系，角速度实际上起到了化学势的作用。利用该热力学势，我们计算了若干物理量，包括该刚性旋转玻色气体的压强、角动量和熵密度、热容、声速以及转动惯量，并将它们表示为温度（$T$）、角速度（$Ω$）和耦合常数（$α$）的函数。我们表明，在高温和大耦合下会出现某些热力学不稳定性。这些不稳定性表现为上述物理量的零值和负值，尤其是转动惯量和热容。转动惯量为零导致在特定$T$或$α$下出现超涡旋现象。超涡旋温度（耦合）随耦合（温度）的增加而降低。我们还观察到在高温和大$α$下出现超光速声速。
英文摘要：
We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature ($T$), angular velocity ($Ω$), and the coupling constant ($α$). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain $T$ or $α$. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high $T$ and for large $α$.
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