  Transition to thermal equilibrium in a uniformly heated two-dimensional
harmonic triangular lattice with nearest neighbor interactions is investigated.
Initial conditions, typical for molecular dynamics simulations, are considered.
Initially, particles have uncorrelated random velocities, corresponding to
initial kinetic temperature of the system, and zero displacements. These
initial conditions can be realized by heating of the system by an ultrafast
laser pulse. In this case, the kinetic temperature of the system oscillates.
The oscillations are caused by the redistribution of energy between kinetic and
potential parts. At large times, energies equilibrate and temperature tends to
the equilibrium value equal to a half of the initial temperature. In our
previous works, an integral exactly describing this transient thermal process
has been derived. The integrand depends on the dispersion relation for the
lattice. The integral contains large parameter, notably time. In the present
work, we investigate large time behavior of the kinetic temperature. Simple
asymptotic expression for deviation of temperature from the steady state value
is derived. The expression contains three harmonics with different frequencies
and amplitudes. Group velocities corresponding to these frequencies are equal
to zero. Two frequencies are close and therefore beats of kinetic temperature
are observed. Amplitude of deviation of temperature from the steady state value
decreases inversely proportional to time. It is shown that the asymptotic
formula has reasonable accuracy even at small times of order of one period of
atomic vibrations.
