Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar-140001, Punjab, India.
Phys Rev E. 2018 Feb;97(2-1):022105. doi: 10.1103/PhysRevE.97.022105.
Motivated by the wide occurrence of limited resources in many real-life systems, we investigate two-lane totally asymmetric simple exclusion process with constrained entrances under finite supply of particles. We analyze the system within the framework of mean-field theory and examine various complex phenomena, including phase separation, phase transition, and symmetry breaking. Based on the theoretical analysis, we analytically derive the phase boundaries for various symmetric as well as asymmetric phases. It has been observed that the symmetry-breaking phenomenon initiates even for very small number of particles in the system. The phases with broken symmetry originates as shock-low density phase under limited resources, which is in contrast to the scenario with infinite number of particles. As expected, the symmetry breaking continues to persist even for higher values of system particles. Seven stationary phases are observed, with three of them exhibiting symmetry-breaking phenomena. The critical values of a total number of system particles, beyond which various symmetrical and asymmetrical phases appear and disappear are identified. Theoretical outcomes are supported by extensive Monte Carlo simulations. Finally, the size-scaling effect and symmetry-breaking phenomenon on the simulation results have also been examined based on particle density histograms.
受许多现实生活系统中资源有限广泛存在的启发，我们研究了具有有限粒子供应的受限入口的两车道完全非对称简单排斥过程。我们在平均场理论的框架内分析了该系统，并研究了各种复杂现象，包括相分离、相变和对称破缺。基于理论分析，我们对各种对称和不对称相的相界进行了分析推导。结果表明，即使在系统中粒子数量非常少时，对称破缺现象也会发生。在有限资源下，对称破缺相起源于激波低密度相，这与具有无限数量粒子的情况形成对比。预期的是，即使对于更高的系统粒子值，对称破缺也会继续存在。观察到七个稳定相，其中三个具有对称破缺现象。确定了出现和消失各种对称和不对称相的系统粒子总数的临界值。理论结果得到了广泛的蒙特卡罗模拟的支持。最后，还基于粒子密度直方图检查了模拟结果的大小缩放效应和对称破缺现象。
