Negative differential mobility in interacting particle systems

Abstract

Driven particles in the presence of crowded environment, obstacles, or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. Based on the empirical studies of conserved lattice gas model, two species exclusion model and other interacting particle systems we propose a new mechanism for complex many-particle systems where slowing down of certain non-driven degrees of freedom by the external field can give rise to NDM. To prove that the slowing down of the non-driven degrees is indeed the underlying cause, we consider several driven diffusive systems including two species exclusion models, misanthrope process, and show from the exact steady state results that NDM indeed appears when some non-driven modes are slowed down deliberately. For clarity, we also provide a simple pedagogical example of two interacting random walkers on a ring which conforms to the proposed scenario.

Assisted exchange models in one dimension

“…For example, the exact large deviation function of the time averaged current resembling to the pressure of an ideal Bose or Fermi gas is obtained in [2], anomalous behavior of cumulants of current near phase transition is shown in [3], universal behavior of current independent of the dimension in symmetric exclusion process connected to reservoirs and its possible generalization to other diffusive systems is discussed in [4]. Also, interesting features like reversal of direction of current with respect to density [5] and negative differential mobility [6][7][8][9] and absolute negative mobility [10][11][12] in interacting particle systems has caused much attention now a days.…”

Multibalance conditions in nonequilibrium steady states

“…To understand the behaviour of current Eq. ( 14), we have plotted J with the bias parameter ε for a particular density ρ = 0.15 and a = 0.2, we found that the current decreases with increase of ε from ε = 3.722 and the gradient becomes negative which give rise to Negative differential response [26] for ε = 3.722 (see Fig. 3).…”

“…We have solved exactly the asymmetric ZRP model in two and three dimensions and show that a factorized steady state (FSS) can be obtained when hop rates satisfy a specific condition. More over, the asymmetric ZRP model (in two dimension) exhibits the phenomena negative differential mobility [26]. We have discussed the steady states obtained by Multibalance for asymmetric finite range process (FRP) with nearest neighbors and as well as next nearest neighbors hopping.…”

“…The specific choice of rates in Eqs. ( 8) and ( 9), give rise to negative differential response [26] of the particles. Following the local detailed balance condition, we can define the driving fields or bias in terms of the asymmetric rate functions as E n i ,n i+1 = ln ur(n i ) u l (n i+1 +1) for the dynamics…”

Absolute negative mobility of active polymer chains in steady laminar flows

“…[54][55][56][57][58][59] Relatively speaking, the phenomenon of negative differential mobility (NDM) can occur in the presence of obstacles or in a crowded environment, where the velocity-force relation shows a nonmonotonic behavior. [60][61][62] Absolute negative mobility (ANM) is a more counterintuitive phenomenon and can only be observed in specific models, where the tracer moves in a direction opposite to that of the driving force. [63][64][65][66][67][68] In steady laminar flows, the phenomenon of ANM can be observed in the systems of passive particles 54,55 or active particles 56 where the persistent motion of the active particles is introduced via a colored noise term.…”