From Anderson Localization to Delocalization in the Nonlinear Hatano-Nelson Model

Weak Kerr-type nonlinearity is known to destroy Anderson localization in Hermitian disordered lattices. Here, we extend this analysis to the non-Hermitian regime using a nonlinear Hatano–Nelson model. We investigate whether an initially localized wavepacket remains confined or delocalizes under the combined influence of asymmetric hoppings and nonlinear interactions. We begin with a linear disordered system in the Anderson-localized regime, where the wavepacket’s second moment saturates over time, confirming localization. Upon introducing nonlinearity, the second moment of the probability distribution over the lattice exhibits unbounded growth, indicating the destruction of Anderson localization, while the distribution’s third moment reveals the asymmetric dynamics of the evolving wavepacket. Our results highlight the intricate interplay of disorder, non-reciprocity, and nonlinear coupling in the dynamics of non-Hermitian systems.