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A<sc>bstract</sc> Recent work has given a systematic way for studying the kinetics of classical weakly interacting waves beyond leading order, having analogies with renormalization in quantum field theory. An important context is weak wave turbulence, occurring for waves which are small in magnitude and weakly interacting, such as those on the surface of the ocean. Here we continue the work of perturbatively computing correlation functions and the kinetic equation in this far-from-equilibrium state. In particular, we obtain the next-to-leading-order kinetic equation for waves with a cubic interaction. Our main result is a simple graphical prescription for the terms in the kinetic equation, at any order in the nonlinearity. 

We consider turbulence of waves interacting weakly via four-wave scattering (sea waves, plasma waves, spin waves, etc.). In the first order in the interaction, a closed kinetic equation has stationary solutions describing turbulent cascades. We show that the higher-order terms generally diverge both at small (IR) and large (UV) wave numbers for direct cascades. The analysis up to the third order identifies the most UV-divergent terms. To gain qualitative analytic control, we sum a subset of the most UV divergent terms, to all orders, giving a perturbation theory free from UV divergence, showing that turbulence becomes independent of the dissipation scale when it goes to zero. On the contrary, the IR divergence (present in the majority of cases) makes the effective coupling parametrically larger than the naive estimate and growing with the pumping scale $L$(similar to anomalous scaling in fluid turbulence). In such cases, the kinetic equation does not describe wave turbulence even of arbitrarily small level at a given $k$if $kL$is large enough that is the cascade is sufficiently long. We show that the character of strong turbulence is determined by whether the effective four-wave interaction is enhanced or suppressed by collective effects. The enhancement possibly signals that strong turbulence is dominated by multiwave bound states (solitons, shocks, cusps), similar to confinement in quantum chromodynamics. Published by the American Physical Society2024 

A bstract It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the wave turbulent state, studying fluctuations about the wave turbulent state. Specifically, we take a classical field theory with an arbitrary quartic interaction and add dissipation and Gaussian-random forcing. Employing the path integral relation between stochastic classical field theories and quantum field theories, we give a prescription, in terms of Feynman diagrams, for computing correlation functions in this system. We explicitly compute the two-point and four-point functions of the field to next-to-leading order in the coupling. Through an appropriate choice of forcing and dissipation, these correspond to correlation functions in the wave turbulent state. In particular, we derive the kinetic equation to next-to-leading order. 

A bstract We compute the amplitude for an excited string in any precisely specified state to decay into another excited string in any precisely specified state, via emission of a tachyon or photon. For generic and highly excited string states, the amplitude is a complicated function of the outgoing kinematic angle, sensitive to the precise state. We compute the square of this amplitude, averaged over polarizations of the ingoing string and summed over polarizations of the outgoing string. The seeming intractability of these calculations is made possible by extracting amplitudes involving excited strings from amplitudes involving tachyons and a large number of photons; the number of photons grows with the complexity of the excited string state. Our work is in the spirit of the broad range of recent studies of statistical mechanics and chaos for quantum many-body systems. The number of different excited string states at a given mass is exponentially large, and our calculation gives the emission amplitude of a single photon from each of the microstates — which, through the Horowitz-Polchinski correspondence principle, are in correspondence with black hole microstates.