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We study the long-time behavior of underdamped Brownian particle movingthrough a viscous medium and in a systematic potential, when it is subjected toa space-dependent high-frequency periodic force. When the frequency is verylarge, much larger than all other relevant system-frequencies, there is aKapitsa time-window wherein the effect of frequency dependent forcing can bereplaced by a static effective potential. Our new analysis includes the casewhen the forcing, in addition to being frequency-dependent, is space-dependentas well. The results of the Kapitsa analysis then lead to additionalcontributions to the effective potential. These are applied to the numericalcalculation of the diffusion coefficient (D) for a Brownian particle moving ina periodic potential. Presented are numerical results, which are in excellentagreement with theoretical predictions and which indicate a significantenhancement of D due to the space-dependent forcing terms. In addition we studythe transport property (current) of underdamped Brownian particles in a ratchetpotential.Comment: RevTex 6 pages, 5 figure

Diffusion enhancement in a periodic potential under high-frequency space-dependent forcing