Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

Abstract

Different thermalization scenarios for systems with large fields have been proposed in the literature based on classical-statistical lattice simulations approximating the underlying quantum dynamics. We investigate the range of validity of these simulations for condensate driven as well as fluctuation dominated initial conditions for the example of a single component scalar field theory. We show that they lead to the same phenomenon of turbulent thermalization for the whole range of (weak) couplings where the classicalstatistical approach is valid. In the turbulent regime we establish the existence of a dual cascade characterized by universal scaling exponents and scaling functions. This complements previous investigations where only the direct energy cascade has been studied for the single component theory. A proposed alternative thermalization scenario for stronger couplings is shown to be beyond the range of validity of classical-statistical simulations.

Attractive versus repulsive interactions in the Bose-Einstein condensation dynamics of relativistic field theories

“…The locations of these peaks correspond to 2n → 2 inelastic scatterings off the "condensate" or off modes with momenta considerably below MðtÞ. Such decay peaks have also been observed in quartic models [32,42]. For instance, the sharp peak of the t ¼ 8000 curve is located at momentum jpj ≈ ffiffi ffi 3 p M ≈ 1, 13 which corresponds to an inelastic scattering of four particles with jpj ≪ M into two particles with energy ϵ ≈ 2M.…”

“…More precisely, in this regime, quantum field theory can be mapped onto a classicalstatistical field theory [33,34], which can be simulated numerically. Otherwise, as soon as typical occupation numbers become of order unity, f ≲ 1, the mapping becomes inaccurate [32,[38][39][40], and the system leaves the classical regime, thermalizing eventually [41]. Thus, we restrict ourselves to the case of sufficiently large occupation numbers and study the scalar systems with classicalstatistical simulations in this section.…”

Fermion production from real-time lattice gauge theory in the classical-statistical regime

“…In this case all results are insensitive to finite changes in the ultraviolet cutoff scale. This insensitivity can be used to verify the applicability of the classical-statistical approach, which has been described in detail in the context of scalar field theory [17]. We emphasize that the classicality condition only restricts the bosonic sector, where the analysis is in complete analogy to previous scalar field theory studies [11,14]: More generally, the classicality condition is met whenever anti-commutator expectation values, such as | ĀĀ |, for typical bosonic field modes are much larger than the corresponding commutators, such as | ÃĀ − AÃ |.…”

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation, and a challenge for kinetic theory

“…In the vicinity of a nonthermal fixed point, strongly correlated quantum systems lose their sensitivity to the initial conditions and other microscopic parameters of the theory [21,22,36]. The single particle distribution function can then be divided into separate scaling regions in momentum space, each of which follows a self-similar evolution…”

“…Another possible reason includes a change of the underlying dynamics, for example, from a perturbative to a nonperturbative mechanism below a characteristic momentum scale. In the context of wave turbulence, each momentum region is usually referred to as an inertial range of momenta, with various examples provided in the literature [20,27,28,36,69,[89][90][91][92].…”