Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model

The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati {\it et.al} does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full lattice ding-a-ling model.Comment: 7 pages, 8 figure

Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices

A previously proposed variational approach for momentum-conserving systems [J. Liu et.al., Phys. Rev. E 91, 042910 (2015)] is extended to systematically investigate general momentum-nonconserving nonlinear lattices. Two intrinsic identities characterizing optimal reference systems are revealed, which enables us to derive explicit expressions for optimal variational parameters. The resulting optimal harmonic reference systems provide information for the band gap as well as the dispersion of renormalized phonons in nonlinear lattices. As a demonstration, we consider the one-dimensional \phi^?4 lattice. By combining the transfer integral operator method, we show that the phonon band gap endows a simple power-law temperature dependence in the weak stochasticity regime where predicted dispersion is reliable by comparing with numerical results. In addition, an exact relation between ensemble averages of the \phi^?4 lattice in the whole temperature range is found, regardless of the existence of the strong stochasticity threshold.Comment: 8 pages, 3 figure