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High-frequency thermal processes in harmonic crystals

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Abstract

We consider two high frequency thermal processes in uniformly heated harmonic crystals relaxing towards equilibrium: (i) equilibration of kinetic and potential energies and (ii) redistribution of energy among spatial directions. Equation describing these processes with deterministic initial conditions is derived. Solution of the equation shows that characteristic time of these processes is of the order of ten periods of atomic vibrations. After that time the system practically reaches the stationary state. It is shown analytically that in harmonic crystals temperature tensor is not isotropic even in the stationary state. As an example, harmonic triangular lattice is considered. Simple formula relating the stationary value of the temperature tensor and initial conditions is derived. The function describing equilibration of kinetic and potential energies is obtained. It is shown that the difference between the energies (Lagrangian) oscillates around zero. Amplitude of these oscillations decays inversely proportional to time. Analytical results are in a good agreement with numerical simulations.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    V. A. Kuzkin & A. M. Krivtsov

  2. Peter the Great Saint-Petersburg Polytechnic University, St. Petersburg, Russia

    V. A. Kuzkin & A. M. Krivtsov

Authors
  1. V. A. Kuzkin
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  2. A. M. Krivtsov
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Correspondence to A. M. Krivtsov.

Additional information

Original Russian Text © V.A. Kuzkin, A.M. Krivtsov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 472, No. 5, pp. 529–533.

The article was translated by the authors.

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Kuzkin, V.A., Krivtsov, A.M. High-frequency thermal processes in harmonic crystals. Dokl. Phys. 62, 85–89 (2017). https://doi.org/10.1134/S1028335817020070

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