Thermodynamic equilibrium of massless fermions with vorticity, chirality and magnetic field

TL;DR

This paper investigates the thermodynamics of massless chiral fermions under vorticity and magnetic fields, revealing quantum effects, exact thermal states, and relationships between vorticity and electromagnetic responses.

Contribution

It extends the non-equilibrium statistical operator method to include quantum effects of vorticity and magnetic fields in chiral fermion systems, deriving exact solutions and interrelations of effects.

Findings

Confirmed known chiral effects like CME, CVE, AVE, and CSE.

Discovered additional second-order effects at thermal vorticity.

Established relations between conductivities of vorticity and magnetic field effects.

Abstract

The present thesis aimed to examine the effects of vorticity on the thermodynamics of relativistic quantum systems. We extend the Zubarev's non-equilibrium statistical operator method to address quantum effects induced by vorticity in the presence of chiral matter and external electromagnetic field and keeping full covariant and quantum properties of the system. To investigate the effects of vorticity, this work has been focused on systems consisting of massless chiral fermions. We recovered the significant quantum phenomena known in the literature, namely the chiral magnetic effect, the chiral vortical effect, the axial vortical effect and the chiral separation effect and we also revealed the presence of additional effects at second-order on thermal vorticity. This study has also identified and presented the exact solutions of thermal states for a system at global thermal equilibrium consisting of chiral massless fermions under the action of an external constant homogeneous magnetic field. Taking advantage of these exact solutions and conservation equations, the study also proved that the thermal coefficients related to first-order effects on thermal vorticity do not receive corrections from the external electromagnetic field. The same argument revealed existing relations between those thermal coefficients, even connecting coefficients related to vorticity to other related to electromagnetic field. For instance, this analysis has found that the chiral vortical effect and the chiral magnetic effect conductivities are connected one to the other by a differential equation. Therefore, this research provides the first steps into deriving the relations between the effects and the interplay of electromagnetic fields and vorticity.