"О ЗАКОНЕ ФУРЬЕ ДЛЯ ЛИНЕЙНОЙ ЦЕПОЧКИ ЧАСТИЦ"
М.В. Гузев (Ин-т прикладной математики ДВО РАН, Владивосток)
Study of temperature distribution and heat flux in a 1D chain of particles motivated by works by Bonetto et al,
Lepri et al in which a homogeneous harmonic chain was proposed to describe thermal effects in an ideal crystal.
It was showed that the Fourier's law is not valid in a stationary state. We analyze thermal effects
in a 1D geometry for arbitrary time based on exact solution of linear equations with initial stochastic conditions.
Spectral characteristics of the basis matrix are calculated with Chebyshev polynomials. The constructed
fundamental solution is written in terms of Bessel functions and generalizes Schrodinger solution for a harmonic
infinite chain. Different integral representations are obtained on complex plane and with the help of Laplace
transformation. The exact solution is used to calculate temperature distribution and heat flux in the chain.
We demonstrated the breakdown of the Fourier's law.