Vortical waves in a quantum fluid with vector, axial, and helical charges. I. Non-dissipative transport

Sergio Morales-Tejera; Victor E. Ambruş; Maxim N. Chernodub

doi:10.1140/epjc/s10052-024-13713-6

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 1320
https://doi.org/10.1140/epjc/s10052-024-13713-6

Regular Article - Theoretical Physics

Vortical waves in a quantum fluid with vector, axial, and helical charges. I. Non-dissipative transport

Sergio Morales-Tejera¹, Victor E. Ambruş¹^a and Maxim N. Chernodub¹^,2^b

¹ Department of Physics, West University of Timişoara, Bd. Vasile Pârvan 4, 300223, Timişoara, Romania
² Institut Denis Poisson, CNRS UMR 7013, Université de Tours, 37200, Tours, France

^a victor.ambrus@e-uvt.ro
^b maxim.chernodub@univ-tours.fr

Received: 5 August 2024
Accepted: 11 December 2024
Published online: 26 December 2024

Abstract

Due to the spin-orbit coupling, Dirac fermions, submerged in a thermal bath with finite macroscopic vorticity, exhibit a spin polarisation along the direction parallel to the vorticity vector $Ω$ $\varvec{\Omega }$ . Due to the symmetries of the Lagrangian for free massless Dirac particles, there are three independent and classically conserved currents corresponding to the vector, axial, and helical charges. The constitutive relations for the charge currents and the stress-energy tensor at thermal equilibrium, derived in the framework of quantum field theory at finite temperature, reveal vorticity-induced contributions that deviate from the perfect fluid form. In this paper, we consider the mode structure of the corresponding hydrodynamical theory and derive collective excitations associated with coherent fluctuations of all three charges. We show that the chirally imbalanced rotating fluid should possess non-reciprocal gapless waves that propagate with different velocities along and opposite to the vorticity vector. We also uncover a strictly unidirectional mode, which we call the axial vortical wave, propagating in the background of the axial charge density. The emergence of this wave can be traced back to earlier studies of vortical chiral fluids in a hydrodynamic approach. We also point out an unexpected instability in the limit of degenerate matter and discuss possible solutions when helicity and axial charge non-conservation are taken into account.

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.