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Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, in analogy with the quantum Bose-Einstein condensation. We report the experimental observation of the…

Optics · Physics 2021-01-04 K. Baudin , A. Fusaro , K. Krupa , J. Garnier , S. Rica , G. Millot , A. Picozzi

Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization, in analogy with the quantum Bose-Einstein condensation. Wave condensation originates in the divergence of…

We present a comprehensive overview of recent advances in theory and experiments on complex light propagation phenomena in nonlinear multimode fibers. On the basis of the wave turbulence theory, we derive kinetic equations describing the…

Recent years have witnessed a resurgence of interest in nonlinear multimode optical systems where a host of intriguing effects have been observed that are impossible in single-mode settings. While nonlinearity can provide a rich environment…

Although the temperature of a thermodynamic system is usually believed to be a positive quantity, under particular conditions, negative temperature equilibrium states are also possible. Negative temperature equilibriums have been observed…

Optics · Physics 2023-02-22 K. Baudin , J. Garnier , A. Fusaro , N. Berti , C. Michel , K. Krupa , G. Millot , A. Picozzi

We consider the free propagation geometry of a light beam (or fluid of light) in a multimode waveguide. As a result of the effective photon-photon interactions, the photon fluid thermalizes to an equilibrium state during its conservative…

We show that the momentum distribution of a nonlinear matter wave suddenly released with a finite velocity in a speckle potential converges, after an out-of-equilibrium evolution, to a universal Rayleigh-Jeans thermal distribution. By…

Disordered Systems and Neural Networks · Physics 2015-12-16 Nicolas Cherroret , Tomasz Karpiuk , Benoît Grémaud , Christian Miniatura

Classical nonlinear waves exhibit, as a general rule, an irreversible process of thermalization toward the Rayleigh-Jeans equilibrium distribution. On the other hand, several recent experiments revealed a remarkable effect of spatial…

We study analytically and numerically the time evolution of a nonlinear field described by the nonlinear Schr\"odinger equation in a chaotic $D$-shape billiard. In absence of nonlinearity the system has standard properties of quantum chaos.…

Statistical Mechanics · Physics 2026-02-06 Leonardo Ermann , Alexei D. Chepelianskii , Dima L. Shepelyansky

We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schr\"odinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans…

Classical nonlinear random waves can exhibit a process of condensation. It originates in the singularity of the Rayleigh-Jeans equilibrium distribution and it is characterized by the macroscopic population of the fundamental mode of the…

Optics · Physics 2020-11-10 J. Garnier , A. Fusaro , K. Baudin , C. Michel , K. Krupa , G. Millot , A. Picozzi

We study the nonlinear chaotic dynamics in a system of linear oscillators coupled by social network links with an additional stratification of oscillator energies, or frequencies, and supplementary nonlinear interactions. It is argued that…

Statistical Mechanics · Physics 2026-03-26 Klaus M. Frahm , Dima L. Shepelyansky

Nonlinear multimode optical systems have attracted substantial attention due to their rich physical properties. Complex interplay between the nonlinear effects and mode couplings makes it difficult to understand the collective dynamics of…

Waves are propagating disturbances that redistribute energy across space. Previous studies have shown that for waves propagating through an inhomogeneously moving mean flow, the conserved quantity is wave action rather than wave energy,…

Fluid Dynamics · Physics 2025-04-29 Zhaohua Wu , Jie Sun , Zhe-Min Tan , Ming Cai , Yongyun Hu , Norden E. Huang

Turbulence in a system of nonlinearly interacting waves is referred to as wave turbulence. It has been known since seminal work by Kolmogorov, that turbulent dynamics is controlled by a directional energy flux through the wavelength scales.…

Fluid Dynamics · Physics 2014-04-07 L. V. Abdurakhimov , I. A. Remizov , A. A. Levchenko , G. V. Kolmakov , Y. V. Lvov

Drawing on classical thermodynamic principles-such as the equipartition of energy and entropy maximization-extensive research has shown that the evolution of optical power in multimode optical systems tends toward a Rayleigh-Jeans…

Thermalization of isolated quantum systems is an intriguing phenomenon at the forefront of contemporary physics. In this work, we demonstrate that nonlinear multimode optical platforms can be harnessed to induce effective quantum…

In an optical experiment, we report a wave turbulence regime that, starting with weakly nonlinear waves with randomized phases, shows an inverse cascade of photons towards the lowest wavenumbers. We show that the cascade is induced by a…

Transitions from turbulence to order are studied experimentally in thin fluid layers and magnetically confined toroidal plasma. It is shown that turbulence self-organizes through the mechanism of spectral condensation. The spectral…

Plasma Physics · Physics 2009-11-10 M. G. Shats , H. Xia , H. Punzmann

We show that a single nonlinear defect can thermalize an initial excitation towards a Rayleigh-Jeans (RJ) state in complex multimoded systems. The thermalization can be hindered by disorder-induced localization phenomena which drive the…

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