VOLUME 84, NUMBER 11 PHYSICAL REVIEW LETTERS 13 MARCH 2000 Normal Heat Conductivity of the One-Dimensional Lattice with Periodic Potential of Nearest-Neighbor Interaction O. V. Gendelman N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, 117977 Moscow, Russia A. V. Savin Institute for Physics and Technology, 119034 Moscow, Russia (Received 16 August 1999) The process of heat conduction in a chain with a periodic potential of nearest-neighbor interaction is investigated by means of molecular dynamics simulation. It is demonstrated that the periodic poten- tial of nearest-neighbor interaction allows one to obtain normal heat conductivity in an isolated one- dimensional chain with conserved momentum. The system exhibits a transition from infinite to normal heat conductivity with the growth of its temperature. The physical reason for normal heat conductivity is the excitation of high-frequency stationary localized rotational modes. These modes absorb the mo- mentum and facilitate locking of the heat flux. PACS numbers: 44.10. + i, 05.45. – a, 05.60. – k, 05.70.Ln The process of heat transport in one-dimensional lattices has become a challenging problem of nonlinear dynamics and statistical physics since the well-known work of Fermi, Pasta, and Ulam (FPU) [1]. They have revealed that weak anharmonicity of nearest-neighbor interaction is not suf- ficient to provide Fourier law of heat conductivity. This result questions the universal validity of the well-known Peierls model of the heat transport in dielectrics [2]. The general reason for the absence of the normal heat conductivity in the system of FPU is its closeness to the exactly integrable weakly nonlinear string described by the Korteveg –de Vries equation. Similarly, the exactly integrable Toda lattice reveals the absence of normal heat conductivity. Thus, the first necessary condition of the nor- mal heat conductivity is stochastic behavior of the system. A widely studied system of this sort is the diatomic Toda lattice (the chain with the exponential potential of nearest- neighbor interaction and altering masses of the par- ticles) [3]. It was demonstrated that this system has no normal heat conductivity at low temperatures even if the mass ratio is unfavorable for the integrability (1:2 [4]). However if the temperature is sufficiently high, the system becomes stochastic and demonstrates normal (linear) temperature distribution along the chain if the temperature gradient is applied. The reason for this effect is the closeness of the diatomic Toda lattice to the integrable Korteveg–de Vries string in the case of low temperatures and to the stochastic diatomic billiard in the case of high temperatures [5]. Recent large-scale numerical simulations had demon- strated that the stochastization of the system is necessary but not sufficient to provide Fourier law in the one- dimensional lattices. For a large variety of chains (FPU with quartic potential and others) exhibiting linear temperature distribution it was demonstrated that the coefficient of the heat conductivity diverges in the thermo- dynamic limit (as the number of particles N in the chain grows) as approximately N 0.37 [6]. Most recently the same situation was proved to be the case for the diatomic Toda lattice [7]. This paper also speculates that the heat conductivity in the linear chain with translationally invari- ant potentials (i.e., with conserved momentum) always diverges. It should be mentioned that for a few studied lattices with on-site potential (i.e., without conservation of momentum) normal heat conductivity is observed (ding-a-dong [8], ding-a-ling [9], and Frenkel-Kontorova models [10,11]). With the above situation in view, the chain with translationally invariant potentials and nor- mal (saturating) heat conductivity may be of essential interest. The present paper deals with the class of chains with the periodic potential of the nearest-neighbor interaction. Such a potential describes, for instance, the relative rotation of polymer fragments around the axis of the macromolecule [12]. This model is rather essential from the physical point of view since the interaction between macromolecules in a polymer crystal is much weaker than intermolecular inter- action. Therefore in many situations the one-dimensional picture of processes in a polymer crystal is of real physi- cal significance rather than of pure academic interest. To the best of our knowledge chains with a periodic poten- tial have not been studied yet from the viewpoint of their heat conductivity. Moreover, the systems of this sort have essential peculiarity, namely, formation of nonlinear local- ized rotational modes [13]. Let us consider a chain of molecules having a fixed distance l between the nearest neighbors. The molecules are allowed to rotate around the chain axis. Let the variable f n t  denote the rotation of the nth molecule around the chain axis in an immovable system of coordinates. Thus a dimensionless Hamiltonian of the system will be H  X n Ω 1 2  f 2 n 1 Uf n11 2f n  æ , (1) 0031-9007 00  84(11)  2381(4)$15.00 © 2000 The American Physical Society 2381