On solving the master equation in spatially periodic systems

摘要: We present a new method for solving the master equation system evolving on spatially periodic network of states. The contains 2ν images “unit cell” n states, arranged along one direction with boundary conditions at ends. analyze structure symmetrized (2νn) × rate constant matrix this and derive recursive scheme determining its eigenvalues eigenvectors, therefore analytically expressing time-dependent probabilities all states in network, based diagonalizations matrices formed by consideration single unit cell. apply our to problem low-temperature, low-occupancy diffusion xenon zeolite silicalite-1 using interstate transitions, transition state theory-based constants previously derived June et al. [J. Phys. Chem. 95, 8866 (1991)]. yields tensor which differs less than 3% from values previ...