标题： 狄拉克费米子的虚数旋转 显示英文标题

标题： Dirac fermions under imaginary rotation

摘要： 本研究中，我们探讨了一组有限倒温度$\beta$和有限化学势$\mu$的自由 Dirac 费米子的性质，这些费米子以虚角速度$\Omega=i\Omega_I$刚性旋转。我们的目的是确定此类状态的解析结构，以及在虚转动条件下得到的结果外推到实转动情况下的前景（和风险）。我们证明，在热力学极限下，系统的状态类似于具有修改后的倒温度$\beta_q = q\beta$和相同化学势的定态系统，其中$q$是不可约分数$\nu = \beta \Omega_I / 2\pi = p/q$的分母。系统的温度成为旋转参数的分数维函数，与标量场的情况类似。化学势破坏了费米子的分数维化。我们还计算了热力学势$\Phi$和相关的热力学函数，表明它们也表现出分数维行为。 最后，我们评估了通过横向平面的轴向和螺旋通量，这些通量是通过涡旋效应产生的，并且表明在 $\nu = 1/q$ 和 $q \to \infty$ 的情况下，它们在热力学极限下发散。 显示英文摘要

摘要： In the present study, we investigate the properties of an ensemble of free Dirac fermions, at finite inverse temperature $\beta$ and finite chemical potential $\mu$, undergoing rigid rotation with an imaginary angular velocity $\Omega=i\Omega_I$. Our purpose is to establish the analytical structure of such states, as well as the prospects (and dangers) of extrapolating results obtained under imaginary rotation to the case of real rotation. We show that in the thermodynamic limit, the state of the system is akin to a stationary system with modified inverse temperature $\beta_q = q\beta$ and the same chemical potential, where $q$ is the denominator of the irreducible fraction $\nu = \beta \Omega_I / 2\pi = p/q$. The temperature of the system becomes a fractal function of the rotation parameter, as in the case of the scalar field. The chemical potential breaks the fractalization of fermions. We also compute the thermodynamic potential $\Phi$ and associated thermodynamic functions, showing that they also exhibit fractal behavior. Finally, we evaluate the axial and helical fluxes through the transverse plane, generated through the vortical effects, and show that they diverge in the thermodynamic limit, in the case when $\nu = 1/q$ and $q \to \infty$.