ABSTRACT
The dynamical properties of nuclei, carried by the concept of phonon quasiparticles , are central to the field of condensed matter. While the harmonic approximation can reproduce a number of properties observed in real crystals, the inclusion of anharmonicity in lattice dynamics is essential to accurately predict properties such as heat transport or thermal expansion. For highly anharmonic systems, non-perturbative approaches are needed, which result in renormalized theories of lattice dynamics. In this article, we apply the Mori-Zwanzig projector formalism to derive an exact generalized Langevin equation describing the quantum dynamics of nuclei in a crystal. By projecting this equation on quasiparticles in reciprocal space, and with results from linear response theory, we obtain a formulation of vibrational spectra that fully accounts for the anharmonicity. Using a mode-coupling approach, we construct a systematic perturbative expansion in which each new order is built to minimize the following ones. With a truncation to the lowest order, we show how to obtain a set of self-consistent equations that can describe the lineshapes of quasiparticles. The only inputs needed for the resulting set of equations are the static Kubo correlation functions, which can be computed using (fully quantum) path-integral molecular dynamics or approximated with (classical or ab initio) molecular dynamics. We illustrate the theory with an application on fcc 4He, an archetypal quantum crystal with very strong anharmonicity.
ABSTRACT
With still limited information on vitamin requirements and considering that many commercial practices adopt dietary vitamin levels above the values suggested by nutritional tables, this study aimed to assess the effect of administering vitamin supplementation to sows in gestation and lactation and to their litters on the reproductive performance and body condition of the sows and on the performance and immune profile of the litters until slaughter. The trial was split into two phases. The first phase used 104 sows, assigned to be randomized to blocks according to parity, submitted until 21 days of lactation to two treatments: control-standard (standard levels of vitamins) and test-elevated (elevated levels of vitamins). Each sow and its respective farrow were considered an experimental unit. The sows underwent evaluations of body condition score, back fat thickness and reproductive performance. In the second phase, 60 barrows and 60 gilts at 21 days of age and mean initial weight of 5.33 ± 1.5 kg until slaughter at 164 days of age. The piglets were assigned to randomized blocks according to the weight and sex of the animals in a 2 × 2 factorial model, with 10 replicates per treatment, where a pen with three animals represented the experimental unit. Following the same treatments of the first phase, the piglets were evaluated for daily weight gain, daily feed intake, feed conversion, mortality rate and humoral immune response. Vitamin supplementation had no positive effects on the reproductive parameters or body composition of sows. However, it positively impacted the performance of the litters in the early nursery stage, but did not lead to superior effects on the immune responses to vaccination against circovirus or mycoplasma.
