Phonon Energies and Lifetimes in Solid Ne and He in the First-Order Self-Consistent Approximation

Abstract

We discuss the response of a crystal in the presence of a neutron distortion in the firstorder self-consistent approximation and we stress the importance of the self-consistency condition. The resultant integral equation for the phonon energies is solved by direct matrix inversion instead of truncating a series expansion. Numerical results are presented for solid Ne and fee He 4 at 10.0 and 11.5 cmVmole.

The phonon absorption line shape of solid molecular H2 and D2 as a function of density

“…Here, as well as in Ref. 23, we also find the secondary peak structure to be largely due to enhanced two-phonon production as discussed in the previous section. The terms beyond the simple three-phonon diagram in Eq.…”

“…Equation (2) for the self-energy can be expressed in closed form and an algebraic equation can be found in Ref. 23. These higher contributions to the self-energy have also been discussed by Ruvalds 25 in connection with two-phonon bound states and resonances.…”

Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

“…The specific choice of Eq. (46), identical for both equations (45), guarantees that if the potential V is quadratic, then the SSCHA tensors (i.e. the SCHA tensors calculated stochastically) (3) Φ and (4) Φ are correctly zero with any finite sampling used to compute the averages.…”

“…Indeed, the necessity of imposing the property (47a) is due to the fact that Eqs. (45) are not symmetric with respect to permutation of indices. That is caused by the arbitrariness in the choice of the variables integrated by parts in the derivation of the formulas, shown in appendix C. As a consequence, an approximate evaluation of the averages causes spurious asymmetries, which are eliminated by applying the projector P perm to the result.…”

“…The theory based on the free energy curvature with respect to the centroids position is 'static' in the sense that there are no dynamical variables evolving with time. However, here we also propose a minimal 'dynamic' extension of the theory that resembles the work by Goldman et al 45 , which allows to study, in a full nonperturbative way, the spectral properties of anharmonic phonons, and thus allows to have finite scattering times and linewidths. This makes the theory able to interpret the results of inelastic scattering processes between anharmonic phonons and external incident particles (typically neutrons), as well as allowing the calculation of the thermal conductivity in strongly anharmonic solids where the harmonic approximation breaks down.…”