Thermal echo in a finite one-dimensional harmonic crystal

Abstract

An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude described by the Bessel function of the first kind. In the present paper it is shown that in the finite crystal this behavior is observed only until a certain period of time when a sharp increase of the oscillations amplitude is realized. This phenomenon, further refereed to as the thermal echo, is realized periodically, with the period proportional to the crystal size. The amplitude for each subsequent echo is lower than for the previous one. It is obtained analytically that the time-dependance of the kinetic temperature can be described by an infinite sum of the Bessel functions with multiple indexes. It is also shown that the thermal echo in the thermodynamic limit is described by the Airy function.

arXiv comment10 pages, 4 figures

References in corpus (8)

• Thermal conduction in classical low-dimensional lattices
• Spatio-temporal isolation of attosecond soft X-ray pulses in the water window
• Fast and slow thermal processes in harmonic scalar lattices
• Discrete breathers assist energy transfer to ac driven nonlinear chains
• Non-stationary heat conduction in one-dimensional chains with conserved momentum
• High-frequency thermal processes in harmonic crystals
• Shockwave Compression and Joule-Thomson Expansion
• On Unsteady Heat Conduction in a Harmonic Crystal

Cited by in corpus (4)

• Unsteady ballistic heat transport in infinite harmonic crystals
• 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
• Approach to thermal equilibrium in harmonic crystals with polyatomic lattice
• Thermal equilibration in a one-dimensional damped harmonic crystal