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Schrodinger equations with non-Hermitian, but PT -symmetric quantum potentials V ( x ) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an “anomalous” refraction index. This turned attention to the nonlinear Schrodinger equations in which the interaction term becomes state-dependent, V ( x ) → W ( ψ ( x ) , x ) . Here, the state-dependence in W ( ψ ( x ) , x ) is assumed logarithmic, and some of the necessary mathematical assumptions, as well as some of the potential phenomenological consequences of this choice are described. Firstly, an elementary single-channel version of the nonlinear logarithmic model is outlined in which the complex self-interaction W ( ψ ( x ) , x ) is regularized via a deformation of the real line of x into a self-consistently constructed complex contour C. The new role played by PT -symmetry is revealed. Secondly, the regularization is sought for a multiplet of equations, coupled via the same nonlinear self-interaction coupling of channels. The resulting mathematical structures are shown to extend the existing range of physics covered by the logarithmic Schrodinger equations.

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels