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We revisit the complex time method for the application to quantum dynamics asan exceptional point is encircled in the parameter space of the Hamiltonian.The basic idea of the complex time method is using complex contour integrationto perform the first-order adiabatic perturbation integral. In this way, thequantum dynamical problem is transformed to a study of singularities in thecomplex time plane -- transition points -- which represent complex degeneraciesof the adiabatic Hamiltonian as the time-dependent parameters defining theencircling contour are analytically continued to complex plane. As anunderlying illustration of the approach we discuss a switch between Rabioscillations and rapid adiabatic passage which occurs upon the encircling of anexceptional point in a special time-symmetric case.

Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space