Blockage-induced condensation controlled by a local reaction

We consider the setup of stationary zero range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows us to control the particle fraction in the condensed phase. This phenomenon results in a current versus blockage parameter curve characterized by two nonanalyticity points.

Figure 1

Stationary particle fraction $\nu$ (at the defect site) vs $q$. Open and solid symbols refer to $L=100$ and $L=1000$, respectively. Circles, squares, and triangles refer, respectively, to $\rho =1$ and $\alpha =0.5$ ($\circ$ and $•, q_{\alpha }=0.33, q_{\rho }=0.50$), $\rho =1.5$ and $\alpha =0.8$ ($\square$ and $\blacksquare , q_{\alpha }=0.23, q_{\rho }=0.60$), and $\rho =2/3$ and $\alpha =0.35$ ($▿$ and $▾, q_{\alpha }=0.30, q_{\rho }=0.40$). Solid lines indicate the analytically predicted behavior in the thermodynamic limit. Dotted lines indicate the values of $q_{\alpha }$.

Figure 2

Stationary current vs $q$. Symbols are as in Fig. 1. Dotted and dashed lines indicate, respectively, the values of $q_{\alpha }$ and $q_{\rho }$.

Figure 3

Stationary occupation number at the defect site and current vs $q$. Open and solid symbols refer to $L=100$ and $L=1000$, respectively. Circles and squares denote the current at $\rho =1$ and $T=1$ ($\circ$ and $•$, value of the current 0.5) and at $\rho =3$ and $T=5$ ($\square$ and $\blacksquare$, value of the current 0.75), whereas triangles and diamonds denote the occupation number at site 1 at $\rho =1$ and $T=1$ ($▿$ and $▾$) and at $\rho =3$ and $T=5$ ($\diamond$ and $⧫$), respectively. Solid and dotted lines indicate, respectively, the analytically predicted behavior of the current and the occupation number in the thermodynamic limit.