Instantons, fluctuations and singularities in the supercritical stochastic nonlinear Schroedinger equation
arXiv:2401.16264 · doi:10.1103/PhysRevLett.133.077202
Abstract
Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use instanton calculus to quantify the effect of extreme fluctuations on the statistics of the energy dissipation rate. While the contribution of the instanton alone is insufficient, we obtain excellent agreement with direct simulations when including Gaussian fluctuations and the corresponding zero mode. Fluctuations are crucial to obtain the correct scaling when quasi-singular events govern the turbulence statistics.
arXiv comment5 pages, 3 figures, 5 pages appendix
References in corpus (21)
- Theory of Bose-Einstein condensation in trapped gases
- Instantons in Burgers Equation
- Instantons and Intermittency
- Viscous Instanton for Burgers' Turbulence
- Intermittency of Burgers' Turbulence
- The instanton method and its numerical implementation in fluid mechanics
- Statistics of soliton-bearing systems with additive noise
- Large negative velocity gradients in Burgers turbulence
- Fast simulation of Gaussian random fields
- Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves
- Origin of heavy tail statistics in equations of the Nonlinear Schrödinger type: an exact result
- Strong Collapse Turbulence in Quintic Nonlinear Schrödinger Equation
- Vorticity statistics in the direct cascade of two-dimensional turbulence
- Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations
- Early stage of integrable turbulence in 1D NLS equation: the semi-classical approach to statistics
- Symmetries and zero modes in sample path large deviations
- Gel'fand-Yaglom type equations for calculating fluctuations around Instantons in stochastic systems
- Instantons for rare events in heavy-tailed distributions
- Path integral derivation and numerical computation of large deviation prefactors for non-equilibrium dynamics through matrix Riccati equations
- Scalable Methods for Computing Sharp Extreme Event Probabilities in Infinite-Dimensional Stochastic Systems
- Computation of minimum action paths of the stochastic nonlinear Schroedinger equation with dissipation