Optical Wave Turbulence: The Conformal Symmetry Transformations of Statistics of the Quantum Fluids of Light
Year: 2025
Type: article
Abstract: We use the quantum fluid analogy [Nazarenko et al., Phys. Rev. E, 92, 2015] for coherent structures (vortices or solitons) interacting among themselves and with the random wave component. This is performed for $2D$ defocusing media based on quantum fluid approximation of the two-dimensional nonlinear Schrödinger equation in the statistical frame. With this, the Lundgren-Monin-Novikov infinite chain of equations for the $n$-point density function $f_n$ for the vorticity field is used. The conformal group of symmetry transformations calculated [Grebenev et. al., Theor. Math. Phys., 217(2), 2023] is applied to implement several elements of a gauge theory in the conformal transformation optics. Finally, we demonstrate how to use the variational generalized Brenier principle [Brenier, J. Am. Math. Soc., 2, 1989] together with the conformal invariance of statistics to close the infinite chain of Landgren-Monin-Novikov equations.
Author: V. N. Grebenev
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411843413