Dirac fermions under imaginary rotation

TL;DR

This paper analyzes free Dirac fermions under imaginary rotation, revealing fractal temperature behavior, divergence of fluxes in the thermodynamic limit, and discussing implications for real rotation extrapolation.

Contribution

It establishes the analytical structure of Dirac fermions under imaginary rotation and explores the fractal nature of thermodynamic quantities and flux divergences.

Findings

Temperature becomes a fractal function of rotation parameter.

Thermodynamic potential exhibits fractal behavior.

Axial and helical fluxes diverge in the thermodynamic limit.

Abstract

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 $q \to \infty$.