Effective phonons in anharmonic lattices: anomalous vs normal heat conduction

– We study heat conduction in one dimensional (1D) anharmonic lattices analytically and numerically by using an effective phonon theory. It is found that every effective phonon mode oscillates quasi-periodically. By weighting the power spectrum of the total heat flux in the Debye formula, we obtain a unified formalism that can explain anomalous heat conduction in momentum conserved lattices without on-site potential and normal heat conduction in lattices with on-site potential. Our results agree very well with numerical ones for existing models such as the Fermi-Pasta-Ulam model, the Frenkel-Kontorova model and the φ model etc. Recent years has witnessed increasing studies on heat conduction in one dimensional (1D) anharmonic (nonlinear) lattices [1]. On the one hand, people would like to know whether or not the Fourier’s law of heat conduction for bulk material is still valid in 1D systems. This is a fundamental question in non-equilibrium statistical mechanics. In fact, it is not trivial at all as a rigorous proof is still not possible. On the other hand, the fast development of nano technology makes it possible to fabricate 1D or quasi 1D systems such as nanowire and/or nanotube etc and to measure its transport properties. To understand heat conduction behavior in such systems is of great interest in heat control and management at nanoscale. Numerically, an anomalous heat conduction heat conductivity diverges with system sizehas been observed in momentum conserved systems without on-site potential such as the Fermi-Pasta-Ulam (FPU) lattice [2], and a normal heat conduction has been found in the systems with on-site potential like the Frenkel-Kontorova model [3] and the φ model [4, 5]. (∗) E-mail: [email protected]