Long-range correlation in driven diffusive systems

Systems driven out of equilibrium often reach a stationary state which
under generic conditions exhibit long-range correlation. As a result
these systems sometimes exhibit properties which are in striking
contrast with equilibrium, such as non-local response to local
perturbation, existence of long-range order and spontaneous symmetry
breaking in one dimension, etc. I shall present two examples from my
work emphasising this aspect of non-equilibrium.

In the first example, I shall discuss the effect of a spatially
localized perturbation which breaks detailed balance, in an otherwise
diffusive system. Such perturbation often leads to long-range
correlation and non-local changes in the stationary state. Our study
is based on a microscopic model where particles on a d-dimensional
lattice interact with symmetric simple exclusion. The system is
brought out of equilibrium by a drive across a single bond in the
bulk. Using an electrostatic analogy I show that the average density
profile and the density-density correlation has a power-law tail.

In the second example, I shall discuss the effect of a localized drive
on the nonequilibrium stationary state of an interface separating two
phases in coexistence. This is done using a spin conserving kinetic
Ising model on a two dimensional lattice with cylindrical boundary
condition, where a drive is applied along a single ring on which the
interface separating the two phases is centered. Unlike the
equilibrium case of a localizing potential, the drive is found to
induce an interface spontaneous symmetry breaking whereby the
magnetization of the driven ring becomes non-zero. The width of the
interface becomes finite and its fluctuation around the driven ring
are non-symmetric. I shall analyze the dynamical origin of these
properties in an adiabatic limit which allows the evaluation of the
large deviation function of the driven-ring magnetization.

Ref:   

[1] Tridib Sadhu, Satya N. Majumdar and David Mukamel, Phys. Rev. E
    84, 051136 (2011)

[2] Tridib Sadhu, Zvi Shapira and David Mukamel,
    Phys. Rev. Lett. 109, 130601 (2012)

[3] Tridib Sadhu, Satya N. Majumdar and David Mukamel, Phys. Rev. E
    90, 012109 (2014)

[4] Tridib Sadhu, Satya N. Majumdar and David Mukamel, J. Phys. A:
    math theo (accepted for publication, 2014)