The Effect Of Solitary Wave Scattering On The Thermal Conductivity Of The System In The One-dimensional FPU-αβ Model

As a basic model, lattice model has been studied to describe the heat conduction of insulating crystal from the microscopic point of view widely and deep since the pioneering work of Debye. At present, for such a system, it is widely believed that energy transports through lattice vibrations which are traditionally rephrased as different type of excitations (such as phonon. soliton and discrete breathers). In this way, the heat conductivity of system crucially depends on both appearing type and scattering law of excitation, which are in turn determined by interparticle interaction, ignoring effects came from external potential, defect, and boundary etc.Nonlinearity is one essential ingredient of interparticle interaction to model real system. If interparticle interaction is simplified as linear potential, there are only linear excitations, i.e., phonons, without interaction. In other words, lattice model degenerates into phonon gas. As a consequence, energy transports in a ballistic way and the divergent exponent of heat conductivity with the system size is 1. This is far from being reality. In the year of 1929, the necessity of nonlinearity is proposed by Peierls who attribute it to phonon interaction and describe the heat transport of crystal by interacting gas of phonons. In addition, the famous paradox of FPU recurrence found by Fermi, Pasta, and Ulam and subsequent related research reveal that nonlinear excitations such as lattice solitons and discrete breathers are ubiquitous besides phonons in nonlinear lattice system, which questions the view that describing the heat transport of crystal by interacting gas of phonons. The current research shows that scattering between lattice solitons and between phonon and DBs play an important role in one-dimensional heat conduction.Asymmetry is another essential ingredient of interparticle interaction to model real system. It induces the thermal expansion effect which is ubiquitous in real systems. Traditional hydrodynamics theory and mode coupling theory revel that the heat conduction behaviors of the model with asymmetric interparticle interaction is qualitatively different from with symmetric interparticle interaction. The recent work of Hong Zhao shows that low dimensional system heat conduction properties are determined by asymmetry of interaction potential. They found that low dimensional system has the normal heat conduction behavior under appropriate degree of asymmetric and certain temperature range, which diverges from the prediction of traditional theory and suggests that the traditional theory is not universal. Unfortunately, the recent research about how asymmetry of interaction potential affects the heat transport of system is insufficient.Based on the above facts, the effect of asymmetry of the interaction potential on the dynamics of solitary wave and heat conduction properties is investigated by numerical simulation in one-dimensional FPU - αβ lattice model, and the connection is found between two effects. This paper would understand the effect of asymmetry of the interaction potential on heat conduction properties of system from the level of the interaction between collective excitation modes.In this paper, we firstly investigate the dynamics of solitary waves in above system by numerical simulation. The main results show as follows:with the increase of asymmetry interaction potential,1) the exciting threshold value increases for Kink, while decreases for Antikink; 2) scattering rates of momentum and energy decreases obviously for the scattering between different types of solitary wave, while for the scattering between same types, it almost no change. In addition, the former is far bigger than the latter; 3) scattering probability increase for scattering of Kink-Antikink and Antikink-Antikink, while decreases for Kink-Kink; 4) the spatial shift increase for the scattering between same types of solitary wave, while decreases for the scattering between different types.Then, we predict that with the increase of asymmetry interaction potential, the heat conduction behavior of system would appear a non-monotonic change by analyzing results of scattering rates of energy and scattering probability. Next, we calculate the heat conductivity of system by Green-Kubo formula which is developed under linear response theory. And the result shows there is a non-monotonic tendency of the change of heat conductivity with the increase of asymmetry parameter. Above result demonstrates the prediction of the dynamics of solitary waves. Our studies have great contribute to understand the effect of asymmetry of the interaction potential on heat conduction properties of system from the level of the interaction between collective excitation modes.