Quantized heat transport in small systems: a phenomenological approach.

Recent progress in nanoscale materials science has pushed the basic research on physical effects while going to such length scales. Particularly, the study of size effects on heat conductivity has attracted much theoretical and experimental interest. In this work we explore the possibilities to study such kinds of phenomena through the quantization of the dynamic equations of a class of nonlinear heat transport macroscopic models. We develop a quantization procedure to search the energy level structure of one-dimensional nanosystems. The procedure may have applications in other fields of the physics of mesoscopic systems.