Strong versus weak wave-turbulence in relativistic field theory

TL;DR

This paper investigates wave turbulence in relativistic scalar field theories across different dimensions, revealing distinct scaling behaviors in weak and strong turbulence regimes through lattice simulations.

Contribution

It provides the first lattice simulation evidence for strong turbulence scaling exponents in relativistic field theories, confirming recent theoretical predictions.

Findings

Weak turbulence exhibits a scaling exponent of d - 3/2.

Strong turbulence in the infrared has a scaling exponent of d + 1.

Simulation results agree with theoretical predictions for both regimes.

Abstract

Nonthermal scaling phenomena can exhibit a characteristic dependence on the dimensionality d of space. For d=3 and 4 we simulate a relativistic scalar field theory on a lattice and compute turbulent scaling exponents. We recover Kolmogorov or weak wave-turbulence in the perturbative high-momentum regime, where it exhibits the scaling exponent kappa_w = d - 3/2. In the nonperturbative infrared regime, we find a different scaling exponent kappa_s = 4 (5) for d=3 (4), which is in agreement with the recently predicted anomalously large values kappa_s = d + 1 of strong turbulence. We show how the latter can be seen to characterize stationary transport of a conserved effective particle number.