𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Frequency Sum Rule and Spectral Moments in Lattice Dynamics

✍ Scribed by V. Frei; P. Deus

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
594 KB
Volume
125
Category
Article
ISSN
0370-1972

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A sum rule of powers of phonon frequencies is derived generalizing a sum rule of squared frequencies given previously by Blackman, Brout, and Rosenstock. The connection of these sums with the moments of the frequency spectrum of the crystal is investigated by choosing gradually enlarged unit cells (GEUC) in the lattice and calculating the sums of the powers of phonon frequencies in suitable points of the correspondingly smaller Brillouin zones. The convergence of these sums in the GEUC‐process is shown using published dispersion curves of cubic crystals and group‐theoretical formulae for the high symmetry points in the Brillouin zones of f.c.c. lattices. Applications of the generalized sum rule are outlined.

πŸ“œ SIMILAR VOLUMES

Frequency moment sum rules, recurrence r
Frequency moment sum rules, recurrence relations and continued fractions in nonequilibrium statistical mechanics
✍ M. Howard Lee πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 783 KB

Dynamical properties of quantum many-body systems, e.g., the electron gas, lattice spins are usually studied via frequency moment sum rules. For example, the dynamic structure factor of the density-density response function in an interacting electron gas can be given a continued fraction expansion i

New nonlinear-laser effects in crystalli
New nonlinear-laser effects in crystalline fine-grained ceramics based on cubic Sc2O3 and Lu2O3 oxides: second and third harmonic generation, and cascaded self-sum-frequency mixing in UV spectral region
✍ A.A. Kaminskii; H. Rhee; H.J. Eichler; K. Ueda; K. Takaichi; A. Shirakawa; M. To πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 183 KB πŸ‘ 1 views

We report on the first observation of the nonlinear cascading Ο‡^(3)^ ↔ Ο‡^(3)^ effects in UV spectral range and second harmonic generation stipulated by the ``defect'' nonlinearity under one-micron pumping in crystalline ceramics based on cubic oxides Sc~2~O~3~ and Lu~2~O~3~. Broadband their multi-wa