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We address the problem of heat conduction in 1-D nonlinear chains; we show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.In recent years a renewed attention has been directed to the energy transport in dynamical systems, a problem which has been denoted by Peierls as one of the outstanding unsolved problems of modern physics [1]. These efforts mainly focused on the possibility to derive the Fourier law of heat conduction on purely dynamical grounds without recourse to any statistical assumption [2][3][4][5][6][7][8][9][10][11]. In spite of relevant progresses, several problems remain open and we are still far from a complete understanding [5][6][7][8][9][10][11].In this paper we investigate a different and important problem namely the possibility to control the energy transport inside a nonlinear 1D chain connecting two thermostats at different temperatures. We show that we can parametrically control the heat flux through the system by acting on a small central part of the chain. Even more interestingly, we show that it is possible to adjust the heat flux by varying the temperatures of both thermostats, keeping constant the temperature difference. Thus we provide a simple mechanism to change the properties of the system, from a normal conductor obeying Fourier law, down to an almost perfect insulator. Controlling heat conduction by nonlinearity opens new possibilities, such as the design of a lattice that carries heats preferentially in one direction, i.e. a thermal rectifier.We consider the Hamiltonianwhich describes a chain of N particles with harmonic coupling of constant K and a Morse on-site potential V n (y n ) = D n (e −αnyn − 1) 2 . This model was introduced for DNA chains where m is the reduced mass of a base pair, y n denotes the stretching from equilibrium position of the hydrogen bonds connecting the two bases of the n-th pair and p n is its momentum [12][13][14]. In the context of the present study, model (1) can simply be viewed as a generic system of anharmonic coupled oscillators, the onsite potential arising from interactions with other parts of the system, not included in the model. The Morse potential is simply an example of a highly anharmonic soft potential, which has a frequency that decreases drastically when the amplitude of the motion increases.In this paper we consider the out-of-equilibrium properties of model (1) by numerically simulating the dynamics of the N particle chain, coupled, at the two ends, with thermal baths at different temperatures T 1 and T 2 . We thermalize at T 1 and T 2 the first and the last L particles by using Nosé-Hoover thermostats chains [15,16],...

DNA is not only an essential object of study for biologists-it also raises very interesting questions for physicists. This paper discuss its nonlinear dynamics, its statistical mechanics, and one of the experiments that one can now perform at the level of a single molecule and which leads to a non-equilibrium transition at the molecular scale.After a review of experimental facts about DNA, we introduce simple models of the molecule and show how they lead to nonlinear localization phenomena that could describe some of the experimental observations. In a second step we analyse the thermal denaturation of DNA, i.e. the separation of the two strands using standard statistical physics tools as well as an analysis based on the properties of a single nonlinear excitation of the model. The last part discusses the mechanical opening of the DNA double helix, performed in single molecule experiments. We show how transition state theory combined with the knowledge of the equilibrium statistical physics of the system can be used to analyse the results.

Many thermodynamic instabilities in one dimension (e.g. DNA thermal denaturation, wetting of interfaces) can be described in terms of simple models involving harmonic coupling between nearest neighbors and an asymmetric on-site potential with a repulsive core, a stable minimum and a flat top. The paper deals with the case of the Morse on-site potential, which can be treated exactly in the continuum limit. Analytical expressions for correlation functions are derived; they are shown to obey scaling; numerical transfer-integral values obtained for a discrete version of the model exhibit the same critical behavior. Furthermore, it is shown in detail that the onset of the transition can be characterized by an entropic stabilization of an -otherwise unstable-, nonlinear field configuration, a soliton-like domain wall (DW) with macroscopic energy content. The statistical mechanics of the DW provides an exact estimate of the critical temperature for a wide range of the discretization parameter; this suggests that the transition can be accurately viewed as being "driven" by a nonlinear entity.

We study a model for the dynamical stretching of DNA which uses the stretching of the hydrogen bonds in a basepair as its main variable. We present a statistical mechanical analysis of the denaturation and specific heat curves, obtained with the transfer integral method; discreteness effects are treated exactly by a numerical solution of the transfer integral operator. Second order self-consistent phonon theory agrees with the exact transfer integral results in the low and intermediate temperature range and explains the phonon softening observed in the molecular dynamics simulations. When the temperature approaches the denaturation temperature, the second order self-consistent phonon results deviate significantly from the exact ones, pointing to the fundamental role of nonlinear processes in DNA denaturation.

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