Quasinormal modes in charged fluids at complex momentum

Abstract

We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordström black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.

Constraints on quasinormal modes and bounds for critical points from pole-skipping

“…In other words, within the complex frequency plane the two lowest-lying QNMs collide with each other on the imaginary frequency axis, as illustrated in the upper two plots in figure 5. Beyond ∆ t however, the relevant critical point of the spectral curve is identified with the level-crossing of QNMs at complex momentum and complex frequency, as it was described previously [10,12,18,31,32,41]. This is illustrated in figure 6.…”

“…However, we expect our results to hold for other theories and other background metrics as well. As an extension of our analysis one may consider the QNMs of the Reissner-Nordström [31,32], the rotating [52] or charged magnetic [53][54][55][56] black branes. It would be interesting to repeat the above computation in theories with gapped half integer spin perturbations corresponding to introducing fermionic operators [25,57,58].…”

“…The pole-skipping phenomenon was first observed as the indication for the hydrodynamic origin of quantum chaotic behavior[16,[19][20][21]. Then it was investigated in many other examples and with distinct motivations[18,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Holographic scalar and vector exchange in OTOCs and pole-skipping phenomena

“…For other progress in holographic studies of pole-skipping points, see for example,[24][25][26][27][28][29][30][31] 3. The pole-skipping points in CFTs were also studied in[28,[35][36][37].…”

Classifying pole-skipping points

“…The existence of pole-skipping for fermions was confirmed in [17]. Other recent development involving pole-skipping include for instance [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In all the above examples, pole-skipping was studied for boundary theories living in a flat spacetime, where one can decompose the bulk perturbations and the boundary Green's function in terms of plane waves.…”