In the past decades, the extensive analytical, numerical and experimental studies have strongly suggested that in the low dimensional (i.e., one and two dimensional) momentum conserving systems, the heat conduction behavior does not follow the Fourier Law and can be classified into several universal classes [1, 2]. However, recently we find that in low dimensional lattices, the asymmetric inter-particle interactions may generally result in the normal heat conduction [3, 4]; Meanwhile, in the lattices without the asymmetric inter-particle interactions, the anomalous heat conduction behavior can be significantly distinct from the known universal classes [5]. These results suggest that it is important to clarify to what an extent the conventional hydrodynamic theories can be applied to the low dimensional heat conduction problem and it is necessary to take into consideration the underlying dynamical mechanisms.

 

[1] S. Lepri, R. Livi, and A. Politi, Phys. Rep. 377, 1(2003)

[2] A. Dhar, Adv. Phys. 57, 457(2008)

[3] Y. Zhong, Y. Zhang, J. Wang, and H. Zhao, Phys. Rev. E 85, 060102(R)(2012)

[4] S.D. Chen, Y. Zhang, J. Wang, and H. Zhao, arXiv: 1204.5933(2012)

[5] D.X. Xiong, Y. Zhang, J. Wang, and H. Zhao, Phys. Rev. E 85, 020102(R)(2012)