Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics

Abstract

We develop the theory of weak wave turbulence in systems described by the Schrödinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the Schrödinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schrödinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schrödinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schrödinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterize such "warm cascade" states.

Langevin based turbulence model and its relationship with Kappa distributions

“…Understanding how these properties emerge from the underlying governing equations is a fundamental challenge in different physics contexts, as aerodynamics 6 , 7 , hydrodynamics 8 , 9 , magnetohydrodynamics 10 , 11 , nematic fluids 12 , nonlinear optics 13 , quantum systems 14 , living matter 15 , medicine 16 and more. Literature on these topics provides examples of different approaches for the study of turbulence.…”

Inverse cascade anomalies in fourth-order Leith models

“…gravity waves on waver surface 17 . Non-classical examples include Kelvin waves on quantized vortex lines 18 , gravitational waves (GW) 19 , waves in fuzzy dark matter 20 or Bose-Einstein condensates (BEC) 21 .…”

“…Self-gravitating dark matter 20 2 or 3 2 -2 0 or a. Kraichnan-Lee vs Kolmogorov-Zakharov solutions. System (4), which includes System…”

“…The nonlinear solutions for η → 1 and for η → ∞ are Appendix A. Rather than computing its non-singular counterpart, it proved more efficient to deal with the original singular system (20).…”

Coherent soliton states hidden in phase-space and stabilized by gravitational incoherent structures

“…There is a surge of interest in studying analogue gravity phenomena in optical laboratory-based experiments that recreate some aspects of the full gravitational system [32][33][34][35][36][37]. Gravity being inherently nonlinear and nonlocal, the hidden coherent soliton states predicted here could be observed in highly nonlocal nonlinear optics experiments [38][39][40][41][42][43][44][45][46][47], or alternatively in dipolar Bose-Einstein condensates [48].…”