We report results from Monte Carlo computations for the average kinetic energy of rare-gas solids (neon, argon, krypton, and xenon), modeled by a Lennard-Jones all-neighbor interaction. The main motivation lies in the recent availability of direct experimental measurements of the average kinetic energy of solid neon, by means of deep-inelastic neutron scattering (DINS). In our computations we take strong advantage in using the effective potential technique, which has been proven to be very useful for systems where quantum effects are not too strong: the path-integral Monte Carlo (PIMC) can be replaced by the classical-like effective-potentia/ Monte Carlo (EPMC), in such a way that the needed computer time is strongly reduced. We resorted to PIMC in the case of neon, due to its rather high quantum effects. Our results for the low-temperature kinetic energy of neon are smaller than the measured ones. This discrepancy could be attributed to the simple model of the interaction we have used, as the agreement with previous theoretical calculations suggests. Moreover, we show that the quantum contributions to the kinetic energy, at the same temperatures used in the abovementioned experiments, are unexpectedly relevant also for argon, krypton, and xenon crystals, so that they should be experimentally detectable as well.
The kinetic energy of solid neon is calculated by a path-integral Monte Carlo approach with a refined Trotter and finite-size extrapolation. These accurate data present significant quantum effects up to temperature Tϭ20 K. They confirm previous simulations and are consistent with recent experiments.
Molecular dynamics calculations performed on a model of a Xe solid with diluted impurities made of I 2 molecules indicate the existence of a Crossover Energy, below which the time to reach thermodynamic equilibrium increases rapidly. This e ect is associated with the existence of long-living out-ofequilibrium states typical of many degrees of freedom Hamiltonian systems at low energies. The possibility of an experimental veri cation of this e ect by laser spectroscopy techniques is also discussed.
We consider the problem of the extrapolation of path-integral Monte Carlo (PIMC) data to infinite Trotter number P. Finite-P data, being even functions of P, have high-P dependence that is generally well described by a quadratic fit, ao + az P, where ao is the exact quantum value.However, in order to get convergence it is often necessary to run PIMC codes with rather high P values, which implies long computer times and larger statistical errors of the data. It is well known that also for harmonic systems the finite-P data are not exact; nevertheless, they can be easily calculated by Gaussian quadrature. Starting from this observation, we suggest an easy way to correct PIMC data for anharmonic systems in order to take into account the harmonic part exactly, with strong improvement of the extrapolation to P = oo. Lower Trotter numbers are thus required, with the advantages of computer-time saving and much better accuracy of the extrapolated values, without any change in the PIMC code. In order to demonstrate the effectiveness of the approach, we report finite-P data processing for a single anharmonic particle, whose finite-P data are obtained by the matrix squaring method, and for a chain of atoms with Morse interaction.
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