Experimental Probing of Non-Fourier Thermal Conductors

Crossover from ballistic to normal heat transport in theϕ4lattice: If nonconservation of momentum is the reason, what is the mechanism?

“…With the development of laser technology [4,5] which allows to probe the thermal properties of materials at reduced size and time scales, ballistic thermal conduction (α = 1) has been observed experimentally for Si 0.9 Ge 0.1 and Si 0.4 Ge 0.6 nanowires, carbon nanotubes, holey silicon, Al 0.1 Ga 0.9 N thin film, and others [6][7][8][9][10][11]. In those studies, this ballistic phonon transport has been found * Electronic address: phyxiongdx@fzu.edu.cn † Electronic address: saadatmand.d@gmail.com ‡ Electronic address: dmitriev.sergey.v@gmail.com for (quasi)-1D samples having length less than a threshold value, L * (usually characterized by the phonon mean free path), such as that for SiGe nanowires L * ≈ 8.3 µm [9], for carbon nanotubes L * ≈ 1 mm [7], and for holey silicon L * ≈ 200 nm [10].…”

“…Thus, these studies suggest that the ballistic thermal conduction in real (quasi-)1D materials can persist over macroscopic distances. In fact, it has been usually believed that in such materials heat is conducted ballistically by the low-frequency, longwavelength phonons [6], and hence the anomalous ballistic behavior can persist even with the presence of defects, isotopic disorders, impurities, and surface absorbates [7].…”

Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source

“…Actually, the specific form of this boundary conditions is not very important in our calculations, since we take large enough N such that the wave reflections from the boundaries do not occur. 6 To obtain a numerical solution in the case of the point source of the heat supply located at i = 0, j = 0, we assume thatb i,j ρ i,j = δ i;0 δ j;0b ρ i,j and use the scheme…”

“…The comparison between numerical solution of stochastic equations and obtained analytical solution demonstrates a very good agreement everywhere except for the main diagonals of the lattice (with respect to the point source position), where the analytical solution is singular.Keywords ballistic heat transfer · 2D harmonic scalar lattice · kinetic temperature 1 Introduction At the macroscale, Fourier's law of heat conduction is widely and successfully used to describe heat transfer processes. However, recent experimental observations demonstrate that Fourier's law is violated at the microscale and nanoscale, in particular, in low-dimensional nanostructures [1][2][3][4][5][6], where the ballistic heat transfer is realized. The anomalous heat transfer also may be related with the spontaneous emergence of long-range correlations; the latter is typical for momentum-conserving systems [7,8].…”

“…− arcsin(tan α sin p 1 ), ±p 1 > 0. (A 6). Applying now formula (A.1), one getsδ 1 (x ⊥ · C) = p 2 − p (j) 2C 0 | cos α| cos p cos arcsin(tan α sin p 1 ) 1+cos arcsin(tan α sin p 1 )1+ tan 2 α (i + tan α j), (A.17) x = x 1 (i + tan α j), (A.18) x ·C p 1 , p (jsign p 1 1 + tan 2 α, (A.19) x ·C p 1 , p |x 1 | 1 + tan 2 α,(A.21) |x| | cos α| = |x 1 |, (A.22) where j = 1, 2.…”