Abstract
We investigate the quantum diffusion of a periodically kicked particle subjecting to both nonlinearity induced self-interactions and PT-symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of mean square of momentum scales with time in a super-exponential form p²(t)∝exp[βexp(α t)], which is faster than any known rates of quantum diffusion. In the PT-symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the interaction strength. The feedback of the intensity-dependent nonlinearity further turns the interaction energy into the kinetic energy, resulting in a super-exponential growth of the mean energy. These theoretical predictions are in good agreement with numerical simulations in a PT-symmetric nonlinear kicked particle. Our discovery establishes a new mechanism of diffusion in interacting and dissipative quantum systems. Important implications and possible experimental observations are discussed.