Strong versus weak wave-turbulence in relativistic field theory

Understand

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.