PHYSICAL REVIEW E 87, 062142 (2013) Heat conduction of symmetric lattices Linru Nie, 1,* Lilong Yu, 1 Zhigang Zheng, 2 and Changzheng Shu 1 1 Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China 2 Department of Physics, Beijing Normal University, Beijing 100082, China (Received 16 December 2012; published 28 June 2013) Heat conduction of symmetric Frenkel-Kontorova (FK) lattices with a coupling displacement was investigated. Through simplifying the model, we derived analytical expression of thermal current of the system in the overdamped case. By means of numerical calculations, the results indicate that: (i) As the coupling displacement d equals to zero, temperature oscillations of the heat baths linked with the lattices can control magnitude and direction of the thermal current; (ii) Whether there is a temperature bias or not, the thermal current oscillates periodically with d , whose amplitudes become greater and greater; (iii) As d is not equal to zero, the thermal current monotonically both increases and decreases with temperature oscillation amplitude of the heat baths, dependent on values of d ; (iv) The coupling displacement also induces nonmonotonic behaviors of the thermal current vs spring constant of the lattice and coupling strength of the lattices; (v) These dynamical behaviors come from interaction of the coupling displacement with periodic potential of the FK lattices. Our results have the implication that the coupling displacement plays a crucial role in the control of heat current. DOI: 10.1103/PhysRevE.87.062142 PACS number(s): 05.40.−a, 07.20.Pe, 05.90.+m I. INTRODUCTION Understanding heat conduction at a molecular level is of fundamental and practical importance [1]. In recent years, much attention has been paid to heat conduction of nonlinear lattice [2] for two reasons. One is that various thermal devices controlling heat flow, such as thermal diodes [3,4], thermal transistors [5], thermal logic gates [6], thermal memories [7], and so on, can be designed theoretically. The other is how these thermal devices may be realized experimentally. The first realization of solid-state thermal diode has been put forward with help of asymmetric nanotubes [8]. Single-photon heat conduction between two resistors coupled weakly to a single superconducting microwave cavity should be experimentally observable [9]. Phonons, as carriers of heat conduction, are by far more difficult to control than electrons and photons. Thus understanding further behavior of phonon and intrinsic mechanism of heat transfer at the molecular level is still an underlying challenge for mankind. According to the thermodynamic second law, heat cannot spontaneously flow from a subsystem at lower temperature to another coupled subsystem at higher temperature. Thus, in order to get a steady heat flow against thermal bias, we must let the system operate away from thermal equilibrium by means of some effective measures. A typical situation is that rocking pe- riodically temperature of one heat bath can direct a steady heat flux from cold bath to hot bath against a nonzero thermal bias in nonlinear lattice junctions [10]. Three necessary conditions for emergence and control of heat current are nonequilibrium source, symmetry breaking, and nonlinearity [11,12]. It is pronounced that thermal rectifying results from symmetry breaking of system. The authors of Ref. [13] studied heat con- duction in anharmonic lattices with mass gradient, and found phenomena of negative differential thermal resistance (NDTR) [14] and thermal rectification [15–18]. In fact, a steady heat current against thermal bias also occurs in symmetric systems. * linrunie@126.com In this paper, we will investigate analytically the heat conduction via two segments of symmetric coupled Frenkel- Kontorova (FK) nonlinear lattices that are sandwiched between two heat baths, and consider effect of coupling displacement between them on heat current. It will be seen that the coupling displacement plays a crucial role in determining magnitude and direction of the heat current. The paper is constructed as follows: First, model and theoretical analysis of heat con- duction of the symmetric system are presented. An analytical expression of heat current will be derived. Then results and discussions are provided. Finally conclusions are made. II. MODEL AND THEORETICAL ANALYSIS Here we study the heat conduction of two segments of coupled Frenkel-Kontorova lattices [19,20] with a coupling displacement, and their two ends contact with two heat baths, respectively. The nonlinear lattices’ Hamiltonian reads H = N 1  i =1  p 2 i 2m + 1 2 k L (q i − q i −1 ) 2 + V L (2π ) 2 cos  2πq i a  + k int 2 (q N 1 +1 − q N 1 + d ) 2 + N  i =N 1 +1  p 2 i 2m + 1 2 k R (q i +1 − q i ) 2 + V R (2π ) 2 cos  2πq i a  , (1) where p i is the momentum for the i th atom, m is the atom mass, the q i = x i − ia denotes the displacement from the equilibrium position ia for the i th atom, a is the lattice period, k L and k R are the spring constants, V L and V R are the on-site potentials a of the FK lattices, k int is the coupling strength between the two segments of FK Lattices, and d is the coupling displacement. The coupling displacement may be formed in the coupling process between the two segments of FK lattices. Depending on the sign of d , the system will tend to bend to left or right. Another physical motivation is based on design 062142-1 1539-3755/2013/87(6)/062142(6) ©2013 American Physical Society