Spatial shift of lattice soliton scattering in the Fermi-Pasta-Ulam model

Suppressed-to-enhanced thermal transport in a Fermi-Pasta-Ulam superlattice: Mediation roles of solitons and phonons

Managing thermal transport in nanostructured materials possesses both theoretical and application value in thermoelectric and microelectronics design. Though a suppressed thermal conductivity could be easily achieved through disorder-induced phonon scattering in a superlattice, it is challenging to enhance thermal transport in a periodically designed lattice. In this paper, we show the possibility of mediating thermal conductivity from a suppressed to an enhanced value in a Fermi-Pasta-Ulam β superlattice with periodic cells of arithmetically increased nonlinearity. When the cell length is increased, thermal conductivity in the superlattice crosses over a suppressed region into an enhanced one and it is even higher than in a homogeneous lattice with the same nonlinearity strength. The mediation originates from the long-lived nonlinear wave packets as solitons across the disorder-induced interface between cells of the superlattice, while at the same time the normal vibrational modes as phonons are suppressed. Our result shows a promising strategy to manipulate thermal transport over a wide range in a superlattice with strong nonlinearity.

Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-αβ lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.

Scattering of lattice solitons and decay of heat-current correlation in the Fermi-Pasta-Ulam-α-β model

As is well known, solitons can be excited in nonlinear lattice systems; however, whether, and if so, how, this kind of nonlinear excitation can affect the energy transport behavior is not yet fully understood. Here we study both the scattering dynamics of solitons and heat transport properties in the Fermi-Pasta-Ulam-α-β model with an asymmetric interparticle interaction. By varying the asymmetry degree of the interaction (characterized by α), we find that (i) for each α there exists a momentum threshold for exciting solitons from which one may infer an α-dependent feature of probability of presentation of solitons at a finite-temperature equilibrium state and (ii) the scattering rate of solitons is sensitively dependent on α. Based on these findings, we conjecture that the scattering between solitons will cause the nonmonotonic α-dependent feature of heat conduction. Fortunately, such a conjecture is indeed verified by our detailed examination of the time decay behavior of the heat current correlation function, but it is only valid for an early time stage. Thus, this result may suggest that solitons can have only a relatively short survival time when exposed in a thermal environment, eventually affecting the heat transport in a short time.