Entropic uncertainty relations for the ground state of a coupled system

There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their quantum numbers. In this work, focussing on the ground state of a nonlinear, coupled Hamiltonian system, we show that approximate eigenstates can be can be constructed within the framework of adiabatic theory. Using the adiabatic eigenstates, we estimate the information entropies and their sum as a function of the the nonlinearity parameter. We also briefly look at the information entropies for the highly excited states in the system.