[Paper Review] Chiral Magnetic-Vortical Wave

David Frenklakh|arXiv (Cornell University)|Oct 30, 2015

High-Energy Particle Collisions Research13 references3 citations

TL;DR

This paper identifies and characterizes the Chiral Magnetic-Vortical Wave (CMVW) in rotating chiral media under external magnetic fields, showing it arises from the vector sum of Chiral Magnetic Wave (CMW) and Chiral Vortical Wave (CVW) velocities. Using hydrodynamic and kinetic theories with relaxation time approximation, it proves the CMVW is non-dissipative in linear order in B and ω, with a purely real dispersion relation.

ABSTRACT

We study collective excitations in rotating chiral media in presence of magnetic field both in hydrodynamic framework and in kinetic theory. We find that the velocity of the mixed Chiral Magnetic-Vortical Wave is a vector sum of velocities of pure Magnetic and Vortical waves which do not exist separately under these conditions. We also use relaxation time approximation to prove that this wave itself is a non-dissipative phenomenon.

Motivation & Objective

• To investigate collective excitations in chiral systems under simultaneous rotation and magnetic fields.
• To determine whether a new hybrid excitation emerges from the interplay of Chiral Magnetic Effect (CME) and Chiral Vortical Effect (CVE).
• To establish the existence and properties of the Chiral Magnetic-Vortical Wave (CMVW) in both hydrodynamic and kinetic frameworks.
• To verify the non-dissipative nature of CMVW in linear order in B and ω using relaxation time approximation (RTA).

Proposed method

• Formulates chiral current densities using CME, CSE, and CVE in the hydrodynamic framework, incorporating axial and vector chemical potentials.
• Derives linearized continuity equations for right-handed fermions with small fluctuations in density and chemical potential.
• Introduces susceptibilities χR/L to relate density and chemical potential fluctuations, leading to a wave equation with effective velocity vR = |B + 2μ₀ω| / (4π²χR).
• Applies kinetic theory to single right-handed Weyl fermions, using the kinetic equation with collision integrals and effective magnetic fields B′± = B ± 2pω.
• Uses the relaxation time approximation (RTA) to solve for distribution function perturbations and derives the dispersion relation νa for the anomalous mode.
• Expands the dispersion relation in powers of B and ω, isolating the first-order (anomalous) term νa and proving its reality, implying non-dissipative behavior.

Experimental results

Research questions

• RQ1 Does a new collective excitation emerge in chiral media when both rotation and magnetic field are present simultaneously?
• RQ2 How does the velocity of this new excitation relate to the individual velocities of the Chiral Magnetic Wave (CMW) and Chiral Vortical Wave (CVW)?
• RQ3 Is the Chiral Magnetic-Vortical Wave (CMVW) dissipative in linear order in B and ω, particularly under the relaxation time approximation?
• RQ4 What is the structure of the dispersion relation for the CMVW, and does it support gapless, non-dissipative modes?

Key findings

• The Chiral Magnetic-Vortical Wave (CMVW) velocity is the vector sum of the pure CMW and CVW velocities, given by vR = |B + 2μ₀ω| / (4π²χR).
• When B + 2μ₀ω = 0, the linear wave velocity vanishes, and non-linear effects dominate, leading to a Hopf-type equation with soliton-like solutions dependent only on vorticity.
• In the relaxation time approximation (RTA), the anomalous part of the dispersion relation νa is purely real, indicating that the CMVW is non-dissipative in linear order in B and ω.
• The dispersion relation for νa is νa = k(B + 2μ₀ω)/(4π²χ) in the long-wavelength limit (kτ ≪ 1), confirming the wave's existence and non-dissipative nature.
• The kinetic theory derivation confirms the hydrodynamic result, showing consistency between hydrodynamic and kinetic frameworks for the CMVW.
• The non-dissipative nature arises because the imaginary part of νa vanishes to linear order in B and ω, even when including collisional relaxation.