Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity

Abstract

We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is non-trivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS in fact becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.

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Cited by in corpus (8)

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• Non-Gibbs states on a Bose-Hubbard lattice
• Enhanced nonreciprocal transmission through a saturable cubic-quintic nonlinear dimer defect
• Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• Thermalization in the one-dimensional Salerno model lattice
• Localization in boundary-driven lattice models
• Dynamics of Holstein polaron in a chain with thermal fluctuations