In the last decade theoretical studies and experimental results on nanoscale phonon transports equally prove that the conductive phonons can be guided in a sense such as electrons. Thus, as an analog of electric devices, it may be possible to prepare thermal diodes (rectifiers) and transistors, thermal logic gates, thermal logic memories or even to exploit the phonon Hall effect. These phenomena give the motivation of the work to be done.
The research has two directions. One of these is the examination of ballistic thermal transport in insulator filaments or two dimensional nanostructures. Within this work the boundary thermal resistance, the phonon scattering on boundary roughness, the material structure and the presumable dynamic phase transitions should be taken into account. The mathematical calculations mean the numerical solution of nonlinear ballistic equations, moreover, the comparison and analysis of the results with the experimental data.
The second direction is the coupling of thermal processes with other transports. It is well known that one of the parameters of Fermi-Dirac statistics is the thermodynamic temperature. It should be examined the effect of ballistic thermal behavior on electron transport both in thin conducting filaments and in two dimensional surfaces at low (few kelvin) or room temperature.
Practice in theoretical and mathematical physics, numerical calculations.