Unraveling the nature of universal dynamics in O(N) theories

Abstract

Many-body quantum systems far from equilibrium can exhibit universal scaling dynamics which defy standard classification schemes. Here, we disentangle the dominant excitations in the universal dynamics of highly-occupied N -component scalar systems using unequal-time correlators. While previous equal-time studies have conjectured the infrared properties to be universal for all N , we clearly identify for the first time two fundamentally different phenomena relevant at different N . We find all N ≥ 3 to be indeed dominated by the same Lorentzian "large-N " peak, whereas N = 1 is characterized instead by a non-Lorentzian peak with different properties, and for N = 2 we see a mixture of two contributions.

Broad excitations in a 2+1D overoccupied gluon plasma

“…This non-Lorentzian peak, thus, appears to be a distinct feature of 2+1D theories in contrast to 3+1D plasmas, where Lorentzian excitations emerge instead [40]. A similar non-Lorentzian shape has been encountered in single-component non-relativistic and relativistic scalar models at low momenta [41,42]. It was also used to distinguish the corresponding excitations from the usual Lorentzian peaks that dominate in O(N )-symmetric scalar models for a large number of components N 1 [42].…”

“…A similar non-Lorentzian shape has been encountered in single-component non-relativistic and relativistic scalar models at low momenta [41,42]. It was also used to distinguish the corresponding excitations from the usual Lorentzian peaks that dominate in O(N )-symmetric scalar models for a large number of components N 1 [42]. For the 2+1D gauge theories considered here, the origin for the observed non-Lorentzian form is currently unknown.…”

“…In practice, the excitation spectrum is studied using the linear response framework built in [39] and first applied in [40] to an isotropic 3+1D gluonic system. A similar classicalstatistical linear response framework has been recently used in scalar theories at self-similar attractors [41,42] and extends classical-statistical simulations in thermal equilibrium that use a fluctuation-dissipation relation explicitly [43,44]. Our work is a natural extension of our previous study of the excitation spectrum of isotropic 3+1D gluodynamics at a classical self-similar attractor [40].…”

“…In the isotropic 3+1D theory, we observed in [40] that the spectral and statistical correlation functions in our considered far-from-equilibrium system are related by the generalized fluctuation-dissipation relation fluctuation-dissipation relation, which for low momenta p T below the temperature reads EE α (ω, p) = Tρ α (ω, p). In contrast, out of equilibrium their connection may be much more complicated or even absent, as observed for scalar theories [41,42,59]. The HTL framework predicts a generalized fluctuation-dissipation relation [60] with a timedependent effective temperature…”

“…If not stated otherwise, the resulting curves are made smoother by employing standard signal processing techniques, as in ref. [42]. To this end we have introduced in eq.…”