Heat conductivity in the presence of a quantized degree of freedom

– We propose a model with a quantized degree of freedom to study the heat transport in quasi-one dimensional system. Our simulations reveal three distinct temperature regimes. In particular, the intermediate regime is characterized by heat conductivity with a temperature exponent γ much greater than 1/2 that was generally found in systems with point-like particles. A dynamical investigation indicates the occurrence of non-equipartition behavior in this regime. Moreover, the corresponding Poincaré section also shows remarkably characteristic patterns, completely different from the cases of point-like particles. The problem of heat conduction in low-dimensional systems has been an interesting subject for a long time due to the potential applications of nanostructured materials and the importance in understanding the physics of low-dimensional systems (see review [1] and the references therein). A long standing issue is the exploration of the necessary condition for a dynamical system to obey the Fourier law [2–6]. For this purpose, a class of “Billiard gas channel” has been proposed recently [7–10] to investigate the connection between macroscopic heat transport and microscopic dynamics. In these models, usually a series of scatterers are placed periodically along two parallel walls, and point-like particles without interaction frequently undergo specular reflections on the boundary formed by the scatterers and the walls. By tracing the motion of the particles, the energy transport in a periodic structure is investigated. Despite intensive simulations in recent years, the sufficient condition for a dynamic system ensuring the Fourier law is still not clear. For example, it was ever found that the system with positive Lyapounov exponent [7] obeys the Fourier law, while the same result was obtained in some linear mixing systems with zero Lyapounov exponent [8–10]. Recently, a modified Lorentz model where particles collide with fixed freely-rotating scatterers was suggested to investigate the heat transport in local thermal equilibrium [11,12]. Normal transport is obtained in such system, indicating that the transport coefficients are finite in the thermodynamic limit. (∗) E-mail:[email protected]