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