We investigate the mean-field energy spectrum and dynamics in a Bose-Einstein condensate in a double-well potential with non-Hermiticity from the nonreciprocal hopping, and show that the interplay of nonreciprocity and nonlinearity leads to exotic properties. Under the two-mode and mean-field approximations, the nonreciprocal generalization of the nonlinear Schrödinger equation and Bloch equations of motion for this system are obtained. We analyze the PT phase diagram and the dynamical stability of fixed points. The reentrance of PT -symmetric phase and the reformation of stable fixed points with increasing the nonreciprocity parameter are found. Besides, we uncover a linear selftrapping effect induced by the nonreciprocity. In the nonlinear case, the self-trapping oscillation is enhanced by the nonreciprocity and then collapses in the PT -broken phase, and can finally be recovered in the reentrant PT -symmetric phase.

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Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems. We study the topological and dynamical properties of the quasiperiodic Su-Schrier-Heeger model with long-range hoppings. It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with non-zero winding numbers ω=1,2, and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length. We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths. The critical exponents extracted from the dynamical behavior agree with the Kibble-Zurek mechanic prediction for the path with W=0.90. In particular, the dynamical exponent of the path crossing the multicritical point is numerical obtained as 1/6∼0.167, which agrees with the unconventional finding in the previously studied XY spin model. Besides, we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.

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