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Out-of-equilibrium one-dimensional disordered dipole chain

We consider a chain of one-dimensional dipole moments connected to two thermal baths with different temperatures. The system is in nonequilibrium steady state and heat flows through it. Assuming that fluctuation of the dipole moment is a small parameter, we develop an analytically solvable model for the problem. The effect of disorder is introduced by randomizing the positions of the dipole moments. We show that the disorder leads to Anderson-like transition from conducting to a thermal insulating state of the chain. It is shown that considered chain supports both ballistic and diffusive heat transports depending on the strength of the disorder. We demonstrate that nonequilibrium leads to the emergence of the long-range order between dipoles along the chain and make the conjecture that the interplay between nonequilibrium and next-to-nearest-neighbor interactions results in the emergence of long-range correlations in low-dimensional classical systems.