An attractor dynamics in a non-Hermitian two-level system

Exceptional point in non-Hermitian system possesses fascinating properties. We present an exactly solvable attractor dynamics for the first time from a two-level dependent Hamiltonian. It allows way to evolve coalescence state pure or mixed initial through varying imaginary parameter along specific diabatic passage. Contrast chaotic that is ultrasensitive condition, designed insensitive conditions. The attractor-like behavior still exists several adiabatic processes.