PHYSICAL REVIEW E 89, 032125 (2014) Asymmetric simple exclusion process on chains with a shortcut Nadezhda Bunzarova, 1, 2 Nina Pesheva, 2 and Jordan Brankov 1, 2 1 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation 2 Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria (Received 2 December 2013; published 21 March 2014) We consider the asymmetric simple exclusion process (TASEP) on an open network consisting of three consecutively coupled macroscopic chain segments with a shortcut between the tail of the first segment and the head of the third one. The model was introduced by Y.-M. Yuan et al. [J. Phys. A 40, 12351 (2007)] to describe directed motion of molecular motors along twisted filaments. We report here unexpected results which revise the previous findings in the case of maximum current through the network. Our theoretical analysis, based on the effective rates’ approximation, shows that the second (shunted) segment can exist in both low- and high-density phases, as well as in the coexistence (shock) phase. Numerical simulations demonstrate that the last option takes place in finite-size networks with head and tail chains of equal length, provided the injection and ejection rates at their external ends are equal and greater than one-half. Then the local density distribution and the nearest-neighbor correlations in the middle chain correspond to a shock phase with completely delocalized domain wall. Upon moving the shortcut to the head or tail of the network, the density profile takes a shape typical of a high- or low-density phase, respectively. Surprisingly, the main quantitative parameters of that shock phase are governed by a positive root of a cubic equation, the coefficients of which linearly depend on the probability of choosing the shortcut. Alternatively, they can be expressed in a universal way through the shortcut current. The unexpected conclusion is that a shortcut in the bulk of a single lane may create traffic jams. DOI: 10.1103/PhysRevE.89.032125 PACS number(s): 05.40.−a, 02.50.Ey, 05.60.−k, 05.70.Ln I. INTRODUCTION The asymmetric simple exclusion process (TASEP) is one of the paradigmatic models for understanding the rich world of nonequilibrium phenomena. Devised to model kinetics of protein synthesis [1], it has found a number of applications for vehicular traffic flow [2], biological transport [3], one- dimensional surface growth [4], forced motion of colloids in narrow channels [5], spintronics [6], transport of “data packets” on the Internet [7], and current through chains of quantum dots [8], to mention a few. Novel features of the TASEP have been found on networks consisting of coupled linear chains with nontrivial geometry. In the approach advanced in our work [9] each macroscopic segment s of the network is considered in a stationary phase determined by its effective injection α ∗ s and ejection β ∗ s rates. Exact in the thermodynamic limit results for the density profile are incorporated. The only molecular-field-type approximation used consists in the neglect of correlations between different chain segments. This allows one to treat the coupling between each two connected segments as coupling to reservoirs with certain effective rates. The possible phase structures of the whole network are obtained as solutions of the resulting set of equations for the effective rates that follow from the continuity of current. The importance of our approach for modeling complex biological transport phenomena was pointed out by Pronina and Kolomeisky [10]. This method became very popular and was used in a number of studies of TASEP and its generalizations on networks with, e.g., junctions, bifurcations, intersections, interacting lanes [11]. Finite-size effects on the density profile due to shifting the position of the double-chain section from the middle of an open network were studied too [12]. Here we consider the TASEP on an open chain with a shortcut in the bulk, introduced as “model A” in Ref. [13]. The current through the shortcut is proportional to a probability q . It is convenient to consider the system as composed of three consecutively connected macroscopic chain segments and a shortcut between the tail of the first segment and the head of the third one; see Fig. 1. In principle, the effect of a shortcut can easily be un- derstood: the decrease in the current through the shunted part (second segment) of the original chain leads to a sharp change of the particle density in the latter. If the chain without a shortcut (q = 0) is in the low-density (L) phase, its bulk density ρ L bulk < 1/2 supports a current J< 1/4. The shortcut takes a part J sc > 0 of that current away from the second segment, hence the current J (2) = J − J sc has to be supported by still less bulk density ρ (2) bulk <ρ L bulk in that segment. Similarly, when the initial chain is in the high-density (H) phase with ρ H bulk > 1/2, the drop in the current through the second segment leads to a still higher bulk density in that segment, ρ (2) bulk >ρ H bulk . Not so simple is the situation when the initial chain is in the maximum current (M) phase with ρ M bulk = 1/2. Now the drop in the current through the shunted segment of the network can be compensated equally well by a decrease or increase in its bulk density. Then the middle segment is forced either in the L or in the H phase, which may also lead to coexistence of the L phase on the left-hand side with the H phase on the right-hand side. This phase structure is additionally favored by the downward (upward) bend in the density profile of the first (third) segment in the maximum current phase. In the case of an open system the coexisting phases are likely to be separated by a completely delocalized domain wall. Such was the situation observed in each of the equivalent segments in a double-chain section incorporated in the middle of a long chain carrying a maximum current [9]. It seems plausible that the above mechanism of influence of the shortcut on the phase state of the shunted segment should 1539-3755/2014/89(3)/032125(7) 032125-1 ©2014 American Physical Society