FIG. 6: Scaling of thermal conductivity. Here we simply apply coordinate transformation ˇ T = T/ 10 to Fig. 5 and then merge it with Fig. 4. One can see the overlap of the two figures, which indicates the scaling of thermal conductivity. II. QUANTUM CORRECTIONS From the experimental point of view, the thermal conductivity of real materials should vanish at zero temperature. This behaviour is inexistent within the classical description of heat conduction as shown above, since the latter leads to a divergent thermal conductivity at zero temperature. The disagreement between the classical description and experimental curves results from the inability of the classical physics to take into account the freezing of phonon modes, which is a pure quantum effect. We would like to emphasize that the consideration of the low temperature regime is not of pure theoretical interest. Generally, the Debye temperature of many solid systems is indeed well above ambient temperature. To name but a few, T$_{D}$ = 783 K in stoichiometric CaB$_{6}$ and T$_{D}$ = 960 K for vacancy doped EuB$_{6}$ [15]. In carbon nanotubes, the Debye temperature may even exceed 1000 − 2000 K [16]. One thus should take into account quantum effects, namely the partial thermalization of phonon modes even far above the room temperature for these materials. 10 GLYPH<s49>GLYPH<s48> GLYPH<s45> GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s45> GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s51> GLYPH<s49>GLYPH<s48> GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s51> GLYPH<s32>GLYPH<s32>GLYPH<s83>GLYPH<s105>GLYPH<s109>GLYPH<s117>GLYPH<s108>GLYPH<s97>GLYPH<s116>GLYPH<s105>GLYPH<s111>GLYPH<s110>GLYPH<s32> GLYPH<s61>GLYPH<s49> GLYPH<s32>GLYPH<s32>GLYPH<s83>GLYPH<s105>GLYPH<s109>GLYPH<s117>GLYPH<s108>GLYPH<s97>GLYPH<s116>GLYPH<s105>GLYPH<s111>GLYPH<s110>GLYPH<s32> GLYPH<s61>GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s44>GLYPH<s32>GLYPH<s115> GLYPH<s99> GLYPH<s97>GLYPH<s108>GLYPH<s101>GLYPH<s32>GLYPH<s99> GLYPH<s104>GLYPH<s97>GLYPH<s110>GLYPH<s103>GLYPH<s101>GLYPH<s32>GLYPH<s119> GLYPH<s105>GLYPH<s116>GLYPH<s104>GLYPH<s32>GLYPH<s84> GLYPH<s47>GLYPH<s49>GLYPH<s48> GLYPH<s84> GLYPH<s32>GLYPH<s32>GLYPH<s83>GLYPH<s67>GLYPH<s80>GLYPH<s84> GLYPH<s32> GLYPH<s61>GLYPH<s49> GLYPH<s32>GLYPH<s32>GLYPH<s83>GLYPH<s67>GLYPH<s80>GLYPH<s84> GLYPH<s32> GLYPH<s61>GLYPH<s48>GLYPH<s46>GLYPH<s49>GLYPH<s44>GLYPH<s32>GLYPH<s115> GLYPH<s99> GLYPH<s97>GLYPH<s108>GLYPH<s101>GLYPH<s32>GLYPH<s99> GLYPH<s104>GLYPH<s97>GLYPH<s110>GLYPH<s103>GLYPH<s101>GLYPH<s32>GLYPH<s119> GLYPH<s105>GLYPH<s116>GLYPH<s104>GLYPH<s32>GLYPH<s84> GLYPH<s47>GLYPH<s49>GLYPH<s48>