Universal Kardar-Parisi-Zhang transient diffusion in nonequilibrium anharmonic chains.

Abstract

The well known nonlinear fluctuating hydrodynamics theory has grouped diffusions in anharmonic chains into two universality classes: one is the Kardar-Parisi-Zhang (KPZ) class for chains with either asymmetric potential or nonzero static pressure and the other is the Gaussian class for chains with symmetric potential at zero static pressure, such as Fermi-Pasta-Ulam-Tsingou (FPUT)-β chains. However, little is known of the nonequilibrium transient diffusion in anharmonic chains. Here, we reveal that the KPZ class is the only universality class for nonequilibrium transient diffusion, manifested as the KPZ scaling of the side peaks of momentum correlation (corresponding to the sound modes correlation), which was completely unexpected in equilibrium FPUT-β chains. The underlying mechanism is that the nonequilibrium soliton dynamics cause nonzero transient pressure so that the sound modes satisfy approximately the noisy Burgers equation, in which the collisions of solitons was proved to yield the KPZ dynamic exponent of the soliton dispersion. Therefore, the unexpected KPZ universality class is obtained in the nonequilibrium transient diffusion in FPUT-β chains and the corresponding carriers of nonequilibrium transient diffusion are attributed to solitons.