Heat conduction in a 1D harmonic chain with three dimensional vibrations.pdf

a r X i v : 0 8 0 6 .4 2 2 4 v 1 [ c o n d - m a t .s t a t - m e c h ] 2 6 J u n 2 0 0 8 Typeset with jpsj2.cls ver.1.2 Full Paper Heat conduction in a 1D harmonic chain with three dimensional vibrations Zonghua Liu1,2 ?, Baowen LI2,3 ? 1Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai, 200062, China 2Department of Physics, Centre for Computational Science and Engineering, National University of Singapore, 117542 Singapore 3NUS Graduate School for Integrative Sciences and Engineering, Singapore 117597, Republic of Singapore (Received June 26, 2008) We study vibrational energy transport in a quasi 1-D harmonic chain with both longitudi- nal and transverse vibrations. We demonstrate via both numerical simulation and theoretic analysis that for 1-D atomic chain connected by 3D harmonic springs, the coefficient of heat conduction changes continuously with its lattice constant, indicating the qualitative differ- ence from the corresponding 1-D case where the coefficient is independent of the lattice constant. KEYWORDS: heat conduction; harmonic chain; 3D vibration; lattice constant; energy transport 1. Introduction Heat conduction in low dimensional systems (less than three dimension) has been attract- ing increasing attention in the past decade.1 From the fundamental point of view, one would like to know whether the fundamental transport theory for bulk material, such as the Fourier law of heat conduction, is still valid for such low dimensional systems. In fact, the question is not trivial, as there is still no rigorous proof available so far. From application point of view, it is an indispensable question to understand the heat conduction properties of the nanoscale materials before they are put into application.2 In order to understand the underlying physical mechanism of heat conduction in one dimensional (1D) systems, different lattice models with and without on-site (pinning) potential have been used, such