Ballistic heat transfer in a one-dimensional crystal with long-range interactions

Non-stationary thermal processes in low-dimensional structures are considered. A previously developed analytical model of ballistic heat transfer is used. The paper focuses on a one-dimensional harmonic crystal with non-nearest neighbour interactions. The coupling forces correspond to the case of a crystal with dipole interactions between the particles. The number of interacting neighbour varies. The dependence of thermal processes on the number of interacting particles has been studied. To describe the evolution of the initial thermal disturbance, an analysis of the dispersion characteristics and group velocities was carried out. It is shown that if only the nearest neighbors are considered, the maximum group velocity will be 78% of the maximum group velocity achieved when considering an infinite number of neighbors. The fundamental solution to the heat propagation problem has been constructed. A solution is obtained for the case of an initial disturbance in the form of a rectangular pulse. An assessment of the influence of neighbours on the rate of heat propagation and on the shape of the heat front was made. The dynamics of changes in wave intensity coefficients depending on the number of neighbors has been revealed. The thermal front is shown to propagate with a finite velocity equal to the maximum group velocity, which increases as more interactions are taken into account. However, the wave intensity factor decreases when the considered neighbours increase. The results obtained in this article aim to describe the heat transfer process in high-purity long-range crystals, such as dipole crystals. The results also help to estimate the error of computer modelling of such processes, since for numerical calculations it is necessary to limit the number of interacting particles.