Time-dependence of the holographic spectral function: diverse routes to thermalisation

Abstract

We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfer of spectral weight to frequencies greater than the initial temperature occurs at an intermediate time (kink formation) and (iii) new peaks with decreasing amplitudes but in greater numbers appear even after the effective temperature has stabilised (persistent oscillations). We find four broad routes to thermalisation for lower values of spatial momenta. At higher values of spatial momenta, kink formations and persistent oscillations are suppressed, and thermalisation time decreases. The general thermalisation pattern is globally top-down, but a closer look reveals complexities.

Exact time dependence of causal correlations and nonequilibrium density matrices in holographic systems

“…More details are presented in the Appendix C . The above prescription reproduces the results obtained with the wellknown Son-Starinets prescription [16] for the thermal retarded correlation [10].…”

“…Further, we obtain the expectation value of the dual operator δ Õ (t, k) from this solution via holographic renormalization [9]. Finally GÕÕ R (t, t , k) is extracted using the relation (3) with f (v, k) chosen to be a narrow Gaussian profile appropriately normalized so that it can be treated as δ(v − t ) up to any required order of numerical accuracy [10]. The latter feature then implies that δ Õ (k) (t) = GÕÕ R (t, t , k).…”

Homogeneous isotropization and equilibration of a strongly coupled plasma with a critical point

“…Another perspective for future investigations consists in going beyond the calculation of one-point functions and study also higher order correlation functions [104][105][106][107][108] in far-from-equilibrium holographic settings. In particular, this kind of study may be of relevance for many different ongoing and future low energy heavy ion experiments, such as the BES program [109] being conducted at RHIC, the future fixed target (FXT) experiments [110,111] also at RHIC, the ongoing HADES experiment [112] at GSI, the future Compressed Baryonic Matter (CBM) experiment at FAIR/GSI [113,114], and also experiments in the future NICA facility [115].…”

Time-dependent NAdS2 holography with applications

“…8 If XðuÞ ≠ 0, it will generate OðuÞ via the Klein-Gordon equation for the dual bulk scalar field. 9 It has been shown in [36] that under similar circumstances the delta function limit where the width of a narrow Gaussian vanishes keeping the impulse fixed can be taken smoothly in numerical holography.…”

“…This assumption is crucial because only with this we get a sensible asymptotic behavior of Φ in the ϵ → 0 limit which can be finally obtained by assembling (20), (21), (35), (36) and (37). This asymptotic expansion turns out to be…”