Jason Laurie

We analyse the dynamics towards partial thermalisation and subsequent cooling in the defocusing two-dimensional nonlinear Schrödinger model, using direct simulations, and insights from the wave-kinetic equation (WKE) and a fourth-order differential approximation model (DAM). We show that the evolving WKE spectrum exhibits two distinct similarity ranges–the quasi-thermal core and the ultraviolet (UV) tail–whereas in the DAM, an additional range of infrared self-similarity appears. By stretching the quasi-thermal region, the self-similar fronts drive an effective dynamical cooling process towards the formal but ill-defined equilibrium state at vanishing temperature—analogous to an UV catastrophe in a system of classical waves.

The statistical evolution of ensembles of random, weakly-interacting waves is governed by wave kinetic equations. To simplify the analysis, one frequently works with reduced differential models of the wave kinetics. However, the conditions for deriving such reduced models are seldom justified self-consistently. Here, we derive a reduced model for the wave kinetics of the Schr{ö}dinger-Helmholtz equations in two spatial dimensions, which constitute a model for the dynamics of light in a spatially-nonlocal, nonlinear optical medium. This model has the property of sharply localising the frequencies of the interacting waves into two pairs, allowing for a rigorous and self-consistent derivation of what we term the semilocal approximation model (SLAM) of the wave kinetic equation. Using the SLAM, we study the stationary spectra of Schr{ö}dinger-Helmholtz wave turbulence, and characterise the spectra that carry energy downscale, and waveaction upscale, in a forced-dissipated setup. The latter involves a nonlocal transfer of waveaction, in which waves at the forcing scale mediate the interactions of waves at every larger scale. This is in contrast to the energy cascade, which involves local scale-by-scale interactions, familiar from other wave turbulent systems and from classical hydrodynamical turbulence.

The statistical evolution of ensembles of random, weakly interacting waves is governed by wave kinetic equations (WKEs). To simplify the analysis, one frequently works with reduced differential models of the wave kinetics. However, the conditions for deriving such reduced models are seldom justified self-consistently. Here, we derive a reduced model for the wave kinetics of the Schrödinger–Helmholtz equations in two spatial dimensions, which constitute a model for the dynamics of light in a spatially nonlocal, nonlinear optical medium. This model has the property of sharply localizing the frequencies of the interacting waves into two pairs, allowing for a rigorous and self-consistent derivation of what we term the semilocal approximation model (SLAM) of the WKE. Using the SLAM, we study the stationary spectra of Schrödinger–Helmholtz wave turbulence, and characterize the spectra that carry energy downscale, and waveaction upscale, in a forced-dissipated setup. The latter involves a nonlocal transfer of waveaction, in which waves at the forcing scale mediate the interactions of waves at every larger scale. This is in contrast to the energy cascade, which involves local scale-by-scale interactions, familiar from other wave turbulent systems and from classical hydrodynamical turbulence.

We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schrödinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic vortices on the background of a spatially infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex.

At the very heart of turbulent fluid flows are many interacting vortices that produce a chaotic and seemingly unpredictable velocity field. Gaining new insight into the complex motion of vortices and how they can lead to topological changes of flows is of fundamental importance in our strive to understand turbulence. Our aim is form an understanding of vortex interactions by investigating the dynamics of point vortex dipoles interacting with a hierarchy of vortex structures using the idealized point vortex model. Motivated by its close analogy to the dynamics of quantum vortices in Bose–Einstein condensates, we present new results on dipole size evolution, stability properties of vortex clusters, and the role of dipole–cluster interactions in turbulent mixing in 2D quantum turbulence. In particular, we discover a mechanism of rapid cluster disintegration analogous to a time-reversed self-similar vortex collapse solution.

It is widely accepted that the primordial universe experienced a brief period of accelerated expansion called inflation. This scenario provides a plausible solution to the horizon and flatness problems. However, the particle physics mechanism responsible for inflation remains speculative with, in particular , the assumption of a scalar field called inflaton. Furthermore, the comparison with the most recent data raises new questions that encourage the consideration of alternative hypotheses. Here, we propose a completely different scenario based on a mechanism whose origins lie in the nonlin-earities of the Einstein field equations. We use the analytical results of weak gravitational wave turbulence to develop a phenomenological theory of strong gravitational wave turbulence where the inverse cascade of wave action plays a key role. In this scenario, the space-time metric excitation triggers an explosive inverse cascade followed by the formation of a condensate in Fourier space whose growth is interpreted as an expansion of the universe. Contrary to the idea that gravitation can only produce a decelerating expansion, our study reveals that gravitational wave turbulence could be a source of inflation. The fossil spectrum that emerges from this scenario is shown to be in agreement with the cosmic microwave background radiation measured by the Planck mission.

It is widely accepted that the primordial universe experienced a brief period of accelerated expansion called inflation. This scenario provides a plausible solution to the horizon and flatness problems. However, the particle physics mechanism responsible for inflation remains speculative with, in particular, the assumption of a scalar field called inflaton. Furthermore, the comparison with the most recent data raises new questions that encourage the consideration of alternative hypotheses. Here, we propose a completely different scenario based on a mechanism whose origins lie in the nonlinearities of the Einstein field equations. We use the analytical results of weak gravitational wave turbulence to develop a phenomenological theory of strong gravitational wave turbulence where the inverse cascade of wave action plays a key role. In this scenario, the space-time metric excitation triggers an explosive inverse cascade followed by the formation of a condensate in Fourier space whose growth is interpreted as an expansion of the universe. Contrary to the idea that gravitation can only produce a decelerating expansion, our study reveals that strong gravitational wave turbulence could be a source of inflation. The fossil spectrum that emerges from this scenario is shown to be in agreement with the cosmic microwave background radiation measured by the Planck mission. Direct numerical simulations can be used to check our predictions and to investigate the question of non-Gaussianity through the measure of intermittency.