Statistical physics of nonlinear wave interaction

Abstract

The thermodynamic properties of vector (O(2) and Complex Spherical) models with four-body interactions are analyzed. When defined in dense topologies, these are effective models for the nonlinear interaction of scalar fields in the presence of a stochastic noise, as has been well established for the case of the mode locking laser formation in a closed cavity. With the help of a novel efficient Monte Carlo algorithm we show how beyond the fully connected case novel and rich phenomenology emerges. Below a certain dilution threshold, the spherical model condensates in a non-equipartite way, while in the XY model the transition becomes continuous and the O(2) symmetry remains unbroken, we attribute this fact to the invariance under local gauge transformations. The introduction of topological inhomogeneities in the network of quadruplets induces novel features: again symmetry conservation; the vanishing of two-point correlators; and a dynamical correlation function presenting two timescales, the large one being related to the transition between different degenerated configurations, connected by nonlocal gauge transformations. We discuss possible experimental implications of these results in the context of nonlinear optics.

21 pages, 24 figures

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• Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models
• Universality class of the mode-locked glassy random laser
• Multi-body quenched disordered $XY$ and $p$-clock models on random graphs
• Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables
• Inverse problem for multi-body interaction of nonlinear waves
• Intensity pseudo-localized phase in the glassy random laser
• Critical properties of disordered XY model on sparse random graphs
• Weak Langmuir turbulence in disordered multimode optical fibers
• Exclusive semileptonic $B$-meson decays using lattice QCD and unitarity
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings
• Mean-field theory of vector spin models on networks with arbitrary degree distributions