Simulation of Quantum Diffusion on a One-Dimensional Periodic Potential

Hydrogen atom diffusion on surfaces is known to be significantly affected by nuclear quantum effects. In this work, we explore the quantum dynamics of hydrogen atom diffusion in a one-dimensional periodic potential model, coupled to a harmonic bath, by using the hierarchical equations of motion (HEOM) approach. The diffusive behavior of an initial Gaussian wavepacket is first characterized by calculating the mean square displacement. We then employ the transfer tensor method to extract from the HEOM result the kernel of a generalized master equation, which describes the coarse-grained evolution of populations across the potential wells. The rate constants from the integral of memory kernels agree with those from direct nonlinear fitting of the population dynamics based on a Markovian master equation, indicating that the long time diffusive behavior can be described by hopping between different potential wells. The results show that, long-range transitions, although having rate constants much smaller than nearest neighbor one, play an important role in determining the diffusion constant.