Anharmonic interaction as random field for thermal transport in FPU-β lattice

We present a stochastic version of the quantum theory for the thermal transport in the Fermi-Pasta–Ulam-β(FPU-β) lattice. In the theory, local bosons (LBs) are introduced as carriers for the transport. The LBs are stimulated by individual atoms in the lattice, which are different from the phonons that are collective motions of the atoms. The LBs move in the FPU lattice and are governed by a set of stochastic differential equations (SDEs). The anharmonic interaction between the atoms in the lattice is transformed to a random field by the Hubbard–Stratonovich transformation, and has been implemented in the set of SDEs. By solving the set of SDEs at the steady state, we study the influence of the anharmonic interaction on the thermal transport. Results show that the anharmonic interaction decreases the thermal current by trapping the LBs on the lattice sites, as well as increases the thermal current by enhancing the amount of the LBs for the transport. The competition between these two mechanisms makes the thermal conductivity of the lattice depend on the anharmonic interaction non-monotonically. The finite size effect of the thermal conductivity has also been captured by the theory.