Evaluation of body condition score measured throughout lactation as an indicator of fertility in dairy cattle

Body condition score (BCS) records of primiparous Holstein cows were analyzed both as a single measure per animal and as repeated measures per sire of cow. The former resulted in a single, average, genetic evaluation for each sire, and the latter resulted in separate genetic evaluations per day of lactation. Repeated measure analysis yielded genetic correlations of less than unity between days of lactation, suggesting that BCS may not be the same trait across lactation. Differences between daily genetic evaluations on d 10 or 30 and subsequent daily evaluations were used to assess BCS change at different stages of lactation. Genetic evaluations for BCS level or change were used to estimate genetic correlations between BCS measures and fertility traits in order to assess the capacity of BCS to predict fertility. Genetic correlation estimates with calving interval and non-return rate were consistently higher for daily BCS than single measure BCS evaluations, but results were not always statistically different. Genetic correlations between BCS change and fertility traits were not significantly different from zero. The product of the accuracy of BCS evaluations with their genetic correlation with the UK fertility index, comprising calving interval and non-return rate, was consistently higher for daily than for single BCS evaluations, by 28 to 53%. This product is associated with the conceptual correlated response in fertility from BCS selection and was highest for early (d 10 to 75) evaluations.</p

Anomalous BCS equation for a Luttinger superconductor

In the context of the Anderson theory of high T_c cuprates, we develop a BCS theory for Luttinger liquids. If the Luttinger interaction is much stronger than the BCS potential we find that the BCS equation is quite modified compared to usual BCS equation for Fermi liquids. In particular T_c predicted by the BCS equation for Luttinger liquids is quite higher than the usual T_c for Fermi liquids

BCS thermal vacuum of fermionic superfluids and its perturbation theory

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon results from the perturbation theory. The BCS thermal vacuum is shown to be a generalized coherent and squeezed state. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase in the parameter space associated with the transformation.Comment: 14 pages, 2 figure

Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions

A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number ($k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em all} $k$ BCs is exactly equivalent to that of the renormalized QAM (with Planck's constant $\hbar ^{\prime}=\hbar /k$) at some {\em fixed} BCs that can be of four types. The quantum cat maps are, up to time reversal, fixed points of the renormalization transformation. Several results at fixed BCs, in particular the existence of a complete basis of ``crystalline'' eigenstates in a classical limit, can then be derived and understood in a simple and transparent way in the general-BCs framework.Comment: REVTEX, 12 pages, 1 table. To appear in Physical Review Letter

Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover

The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc obtained when neglecting screening effects. Subsequent work on this topic, aimed at extending the original GMB argument away from the BCS limit with diagrammatic methods, has kept this disentangling between pairing and screening throughout the BCS-BEC crossover, without realising that the conditions for it to be valid are soon violated away from the BCS limit. Here, we reconsider this problem from a more general perspective and argue that pairing and screening are intrinsically entangled with each other along the whole BCS-BEC crossover but for the BCS limit considered by GMB. We perform a detailed numerical calculation of the GMB diagrammatic contribution extended to the whole BCS-BEC crossover, where the full wave-vector and frequency dependence occurring in the repeated in-medium two-particle scattering is duly taken into account. Our numerical calculations are tested against analytic results available in both the BCS and BEC limits, and the contribution of the GMB diagrammatic term to the scattering length of composite bosons in the BEC limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find that it agrees quite well with Quantum Monte Carlo calculations and experimental data available in the unitarity regime.Comment: 21 pages, 11 figure

Absence of coherent peaks in a Z2Z_{2} fractionalized BCS superconducting state

We explore a $Z_{2}$ fractionalized Bardeen-Cooper-Schrieffer (BCS) superconducting state, which is a minimal extension of usual BCS framework. It is found that this state has similar thermal and transport properties, but its single-particle feature strongly deviates from the coherent quasiparticle behavior of the classic/conventional BCS superconducting state. The fingerprint of such $Z_{2}$ BCS state is the absence of the BCS coherent peaks and instead a kink in the local density of state occurs, which in principle could be probed by scanning tunneling microscopy or point-contact spectroscopy experiments. The corresponding exactly soluble models that realize the desirable $Z_{2}$ fractionalized BCS state is presented. In addition, we also study the extended $t$-$U$-$J$ model by using $Z_{2}$ slave-spin representation and find that the $Z_{2}$ BCS state may exist when the paring structure is fully gapped or has nodes. The prototypical wave-function of such a $Z_{2}$ BCS state is also proposed, which could be taken as trial wave-function in current numerical techniques. The present work may be helpful to further study the unconventional superconductivity and its relation to non-Fermi liquids.Comment: 7 pages,5 figure,more discussions adde