Relaxation times for chiral transport phenomena and spin polarization in a strongly coupled plasma

We compute the dynamical relaxation times for chiral transport phenomena in a strongly coupled regime using the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. These relaxation times can be a useful proxy for the dynamical timescale for achieving equilibrium spin polarization of quasiparticles in the presence of a magnetic field and fluid vorticity. We identify the Kubo relations for these relaxation times and clarify some previous issues regarding time dependence of the chiral vortical effect. We study the consequences of imposing time-reversal invariance on parity-odd thermal noise fluctuations that are related to chiral transport coefficients by the fluctuation-dissipation relation. We find that time-reversal invariance dictates the equality between some of the chiral transport coefficients as well as their relaxation times.

Figure 1

The real (red) and imaginary (blue) parts of ${\tilde{\sigma }}_B(k)$ with $2\pi T/\mu =95$ when $|\mathit{k}|=0.1$ as a function of frequency.

Figure 2

The real (red) and imaginary (blue) parts of ${\tilde{\sigma }}_V(k)$ with $2\pi T/\mu =95$ when $|\mathit{k}|=0.1$ as a function of frequency.

Figure 3

The frequency-dependent chiral transport coefficients that are obtained by appropriately removing the shear-diffusion pole structures from the retarded correlation functions. The red and blue curves show the real and the imaginary parts respectively.

Figure 4

The numerical result for the relaxation times of chiral transport phenomena as a function of $\tau =\frac{2\pi T}{\mu }$.