Thermalization of the Ablowitz-Ladik lattice in the presence of non-integrable perturbations

We investigate the statistical mechanics of the photonic Ablowitz-Ladik lattice, the integrable version of the discrete nonlinear Schrodinger equation. In this regard, we demon-strate that in the presence of perturbations, the complex response of this system can be accurately captured within the framework of optical thermodynamics. Along these lines, we shed light on the true relevance of chaos in the thermal-ization of the Ablowitz-Ladik system. Our results indicate that when linear and nonlinear perturbations are incorpo-rated, this weakly nonlinear lattice will thermalize into a proper Rayleigh-Jeans distribution with a well-defined tem-perature and chemical potential, in spite of the fact that the underlying nonlinearity is non-local and hence does not have a multi-wave mixing representation. This result illustrates that in the supermode basis, a non-local and non-Hermitian nonlinearity can in fact properly thermalize this periodic array in the presence of two quasi-conserved quantities. (c) 2023 Optica Publishing Group