Negative mobility induced by colored thermal fluctuations

Anomalous transport of non-Markovian thermal Brownian particle dynamics in spatially periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is modeled by a generalized Langevin equation with exponentially correlated Gaussian thermal noise, obeying the fluctuation-dissipation theorem. We study the role of nonzero correlation time of thermal fluctuations for the occurrence of absolute negative (linear) mobility (ANM) near zero bias, negative-valued, nonlinear mobility (NNM), and negative differential mobility (NDM) at finite bias away from equilibrium. We detect that a nonzero thermal correlation time can either enhance or also diminish the value of ANM. Moreover, finite thermal noise correlation can induce NDM and NNM in regions of parameter space for which such ANM and NNM behaviors are distinctly absent for limiting white thermal noise. In parts of the parameter space, we find a complex structure of regions of linear and nonlinear negative mobility: islands and tongues which emerge and vanish under parameters manipulation. While certain such anomalous transport regimes fade away with increasing temperature some specific regions interestingly remain rather robust. Outside those regimes with anomalous mobility, the ac/dc driven transport is either normal or the driven Brownian particles are not transported at all.

Figure 1

(Color online) Illustration of destructive role of finite thermal noise correlations on absolute negative mobility (ANM): The averaged long-time velocity $v$ of the ac driven Brownian particle is depicted as a function of the externally applied, static force $f$. The chosen system parameters are $a=4.578$, $\omega =4.9$, $\gamma =0.9$, and $D=0.001$. While white thermal noise $\left({\tau }_c=0\right)$ does depict ANM this is increasingly diminished upon increasing the correlation time of thermal noise until it merges into a normal positive mobility behavior.

Figure 2

(Color online) Illustration of constructive role of thermal noise correlations on absolute negative mobility: The averaged long-time velocity $v$ of the Brownian particle is depicted as a function of the bias force $f$ for selected values of the noise correlation time ${\tau }_c$ of thermal fluctuations. The system parameters are different from Fig. 1 and read $a=4.1293$, $\omega =4.9$, $\gamma =0.9$, and $D=0.001$. (a) Within this regime we find that a small thermal noise correlation time can enhance ANM. (b) Upon further increasing thermal noise correlation time ${\tau }_c$ from the values shown in (a) we observe a turnover into ANM again (case ${\tau }_c=0.07$); followed by a NNM behavior $\left({\tau }_c=0.0985\right)$. Finally reentry into a normal transport regime is observed at small bias with a regime exhibiting NDM as $f$ is increased further $\left({\tau }_c=0.12\right)$.

Figure 3

(Color online) Regions of negative (nonlinear) mobility manifested either as ANM or also NNM, in the parameter plane given by $\left\{a,{\tau }_c\right\}$ for three different temperatures, $D=0.0001,0.001,0.01$ (top to bottom). The remaining parameters are fixed: namely, $a=4.1293$, $\omega =4.9$, $\gamma =0.9$, and $f=0.1$.

Figure 4

(Color online) Role of nonzero thermal noise correlations on absolute negative mobility for a parameter set corresponding to the anomalous Josephson-junction transport regime used in the experiment in Ref. [8]. The long-time averaged voltage $v$ across the junction is depicted as a function of the externally applied dc current $f$. The corresponding dimensionless parameters are $a=13.874$, $\omega =2.75$, $\gamma =2.264$, and $D=0.000895$. The white thermal noise regime (i.e., ${\tau }_c=0$) depicts ANM behavior which is sustained for short correlation times of the thermal noise. For increasingly larger correlation times ANM is diminished and eventually vanishes all together and crosses over into a normal positive mobility behavior. Still, negative-valued, nonlinear mobility can occur far away from equilibrium; note the nonlinear response behavior for $\tau =0.02$ and around $f\sim 0.6$.