  The transport properties of Brownian ratchet was studied in the presence of
stochastic intensity noise (SIN) in both overdamped and underdamped regimes. In
the overdamped case, analytical solution using the matrix continued fraction
method revealed the existence of a maximum current when the noise intensity
fluctuates on intermediate time scale regions. Similar effects were observed
for the underdamped case by Monte Carlo simulations. The optimal
time-correlation for the Brownian transport coincided with the experimentally
observed time-correlation of the extrinsic noise in Esherichia coli gene
expression and implied the importance of environmental noise for molecular
mechanisms.
