Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential

In this study we used nonequilibrium simulation method to investigate the temperature dependent divergence of thermal conductivity in one dimensional momentum conserving system with asymmetric double well nearest-neighbor interaction potential. We show that the value of divergence exponent ($\alpha$) in the power law divergence of thermal conductivity depends on the temperature of the system. At low and high temperatures $\alpha$ reaches close to $\sim0.5$ and $\sim0.33$ respectively. Whereas in the intermediate temperature the divergence of thermal conductivity with the chain length saturates with $\alpha\sim0.07$. Subsequent analysis showed that the predicted value of $\alpha$ in the intermediate temperature may not have reached its thermodynamic limit. Further calculations of local $\alpha$ revealed that its approach towards the thermodynamic limit crucially dependent on the temperature of the system. At low and high temperatures local $\alpha$ reaches its thermodynamic limits in shorter chain lengths. On the contrary in case of intermediate temperature it's progress towards the asymptotic limit is nonmonotonous.