Geodesic
Oscillatory-damping temperature behavior in one-dimensional harmonic model of a perfect crystal
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 170-179

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We constructed an analytical solution for the equations modeling a one-dimensional harmonic crystal. The solution is used to calculate the temperature as a measure of kinetic energy. For stochastic initial conditions, we obtain a law of temperature distribution which differs from the Fourier law. It is demonstrated that the correlations linking the position of the particles leads to the appearance of harmonics at twice the frequency compared with the main oscillation generated due to correlations between the initial velocities. 
@article{DVMG_2017_17_2_a4,
     author = {M. A. Guzev and A. A. Dmitriev},
     title = {Oscillatory-damping temperature behavior in one-dimensional harmonic model of a perfect crystal},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {170--179},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a4/}
}
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M. A. Guzev; A. A. Dmitriev. Oscillatory-damping temperature behavior in one-dimensional harmonic model of a perfect crystal. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 170-179. http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a4/