Inverse cascade anomalies in fourth-order Leith models

We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

On the connection between intermittency and dissipation in ocean turbulence: a multifractal approach

The multifractal theory of turbulence is used to investigate the energy cascade in the Northwestern Atlantic ocean. The statistics of singularity exponents of horizontal velocity gradients computed from in situ measurements at 2 km resolution are used to characterize the anomalous scaling of the velocity structure functions at depths between 50 ad 500 m. Here, we show that the degree of anomalous scaling can be quantified using singularity exponents. Observations reveal, on one side, that the anomalous scaling has a linear dependence on the exponent characterizing the strongest velocity gradient and, on the other side, that the slope of this linear dependence decreases with depth. Since the observed distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade, the log-Poisson model, to derive the functional dependence of the anomalous scaling with the exponent of the strongest velocity gradient, as well as the dependence with dissipation. Using this model we can interpret the vertical change of the linear slope between the anomalous scaling and the exponents of the strongest velocity gradients as a change in the energy cascade. This interpretation assumes the validity of the multifractal theory of turbulence, which has been assessed in previous studies.

Critical non-Hermitian skin effect

Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

Anomalous Scaling in the Kinematic Magnetohydrodynamic Turbulence

The problem of the anomalous scaling in the kinematic magnetohydrodynamic turbulence is investigated using the field theoretic renormalization group method and the operator product expansion technique. The anomalous dimensions of all leading composite operators, which drive the anomalous scaling of the correlation functions of a weak passive magnetic field, are determined up to the second order of the perturbation theory (i.e., in the two-loop approximation in the field theoretic terminology) in the presence of a large scale anisotropy for physically the most interesting three-dimensional case. It is shown that the leading role in the anomalous scaling properties of the model is played by the anomalous dimensions of the composite operators near the isotropic shell, in accordance with the Kolmogorov’s local isotropy restoration hypothesis. The importance of the two-loop corrections to the anomalous dimensions of the leading composite operators is demonstrated.