Stokes phenomenon of a three-modes non-Hermitian quantum system

Abstract The dynamics of a three-modes non-Hermitian quantum system with a periodical-driving are studied. The Stokes phenomenon is observed in the adiabatic approximation. It is shown that the multiplier of the exponentially dominant eigenstate in the evolving state may be negligible and the multiplier of the exponentially small eigenstate in the evolving state may appear or disappear and oscillates drastically. Such Stokes phenomenon is independent of whether or not the exceptional point is encircled. The origin of such Stokes phenomenon is from the imaginary part of the complex eigenenergies. The eigenstate with the maximum imaginary part of dynamical phase factor in the evolving state will inevitably mask the other eigenstates. We also estimate the range of driving-frequency for the adiabatic approximation condition. The contribution is primarily theoretical in nature.