The quantum dynamics of a Xe atom placed on the STM surfaceis studied considering two important types of nonstationary externalforces. These are the driving forces appearing during the application of avoltage pulse, and the fluctuating forces determined by the coupling to anOhmic environment. The localization probability on the tipduring voltage pulses of 20 and 7 ns with symmetric triangular andtrapezoidal shapes is calculated neglecting the environmental interactions.The results indicate that the atom dynamics in this case is reversible, andafter the pulse the transfer probability is small.The effects of the fluctuating forces produced by the coupling to thesurrounding electrons and surface phonons are studied in a static potential.It is shown that the thermal fluctuations at the environmental temperaturecan lead to irreversible atom tunneling through the potential barrier,described by an exponential decay law.PACS Nos.: 61.16.Di, 73.40.Gk, 05.40.+j