Temperature Interfaces in the Katz-Lebowitz-Spohn Driven Lattice Gas

Authors: Ruslan I. Mukhamadiarov, Priyanka, Uwe C. Tauber
Department of Physics and Center for Soft Matter and Biological Physics,
Virginia Tech, Blacksburg, VA

We explore the intriguing spatial patterns that emerge in a two-dimensional 
spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with 
attractive nearest-neighbor interactions. The domain is split into two 
regions with hopping rates governed by different temperatures T > T_c and 
T_c, respectively, where T_c indicates the critical temperature for phase 
ordering, and with the temperature boundaries oriented perpendicular to the 
drive. In the hotter region, the system behaves like the (totally) asymmetric
exclusion processes (TASEP), and experiences particle blockage in front of 
the interface to the critical region.

To explain this particle density 
accumulation near the interface, we have measured the steady-state current in
the KLS model at T > T_c and found it to decay as 1/T. In analogy with TASEP 
systems containing "slow" bonds, transport in the high-temperature subsystem 
is impeded by the lower current in the cooler region, which tends to set the 
global stationary particle current value. This blockage is induced by the 
extended particle clusters, growing logarithmically with system size, in the 
critical region. We observe the density profiles in both high-and low-
temperature subsystems to be similar to the well-characterized coexistence 
and maximal-current phases in (T)ASEP models with open boundary conditions, 
which are respectively governed by hyperbolic and trigonometric tangent 
functions. Yet if the lower temperature is set to T_c, we detect marked 
fluctuation corrections to the mean-field density profiles, e.g., the 
corresponding critical KLS power law density decay near the interfaces into 
the cooler region. If the temperature interface is aligened parallel to the
drive, we observe the cooler region to act as an absorbing sink for particle 
transport, with blockages emerging at the subsystem boundaries.

Ref.: R.I. Mukhamadiarov, Priyanka, and U.C.T., arXiv:1907.08576

Research was sponsored by the Army Research Office (ARO) and was accomplished
under Grant Number W911NF-17-1-0156.