Journal
PHYSICAL REVIEW E
Volume 79, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.79.041137
Keywords
diffusion; Fokker-Planck equation; random processes
Categories
Funding
- Ministry of Education and Research of the Republic of Estonia [SF0690030s09]
- Estonian Science Foundation [7466]
- Spanish MICINN
- FEDER [FIS2007-60327]
- EU [LSHB-CT2004-005137]
- DFG [SFB-486]
- Volkswagen Foundation [I/80424]
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The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the influence of a time-periodic rectangular force. As a main result, we show that such a force does not affect the universal scaling relation between the anomalous current and diffusion when applied to the biased dynamics: in the long-time limit, subdiffusion current and anomalous diffusion are immune to the driving. This is in sharp contrast with the unbiased case when the subdiffusion coefficient can be strongly enhanced, i.e., a zero-frequency response to a periodic driving is present.
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