2004/04/09 by Vladimir N. Likhachev, В. Н. Лихачев, Likhachev, Vladimir N. +5
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Thermal properties of materials #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0404223
9 pages, 3 figures
arxiv created 2004/04/09 · openalex publication_date 2004/04/09 · arxiv updated 2009/12/01 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
In the present communication we consider the one-dimensional (1D)\nisotopically disordered lattice with the harmonic potential. Our analytical\nmethod is adequate for any 1D lattice where potential energy can be presented\nas the quadratic form U= frac12 \∑i,j q(i) Uij q(j), where q(i) --\ncoordinate or velocity of i-th particle. There are derived the closed system\nof equations for the temporal behavior of the correlation functions. The final\nexpressions allow to calculate the kinetics and dynamics of the system --\nenergy, temperature profile, thermal conduction and others. There is developed\nthe method for the calculation of the evolution of the eigenvalues\n(frequencies) and eigenvectors (relaxation times) to their stationary values.\nExact results are obtained for times \≃ 1014. The methods are\nsuggested allowing to extend the range of the relaxation times upto \≃\n1028. The spectrum of relaxation times reaches it constant value starting\nfrom the number of particles N in the lattice N \≥ 300. Thermal\nconductance \κ has the non-monotonic character: for the number of\nparticles N < 300 \κ increases as \κ \≃ 2.4 lg N, reaches\nthe maximum value equal \≃ 4.0 at N \≃ 300 and then slowly\ndecreases upto N = 700. The stationary state is unique and satisfies the\nGibbs distribution. An excellent agreement between numerical simulations and\nanalytical results is obtained where possible.\n