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Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.

Methane produced from 35 Aberdeen-Angus and 33 Limousin cross steers was measured in respiration chambers. Each group was split to receive either a medium- or high-concentrate diet. Ruminal digesta samples were subsequently removed to investigate correlations between methane emissions and the rumen microbial community, as measured by qPCR of 16S or 18S rRNA genes. Diet had the greatest influence on methane emissions. The high-concentrate diet resulted in lower methane emissions (P < 0.001) than the medium-concentrate diet. Methane was correlated, irrespective of breed, with the abundance of archaea (R = 0.39), bacteria (−0.47), protozoa (0.45), Bacteroidetes (−0.37) and Clostridium Cluster XIVa (−0.35). The archaea:bacteria ratio provided a stronger correlation (0.49). A similar correlation was found with digesta samples taken 2–3 weeks later at slaughter. This finding could help enable greenhouse gas emissions of large animal cohorts to be predicted from samples taken conveniently in the abattoir.

The aims of the present study were to quantify hydrogen (H 2 ) and methane (CH 4 ) emissions from beef cattle under different dietary conditions and to assess how cattle genotype and rumen microbial community affected these emissions. A total of thirty-six Aberdeen Angus-sired (AAx) and thirty-six Limousin-sired (LIMx) steers were fed two diets with forage:concentrate ratios (DM basis) of either 8:92 (concentrate) or 52:48 (mixed). Each diet was fed to eighteen animals of each genotype. Methane (CH 4 ) and H 2 emissions were measured individually in indirect respiration chambers. H 2 emissions (mmol/min) varied greatly throughout the day, being highest after feed consumption, and averaged about 0·10 mol H 2 /mol CH 4 . Higher H 2 emissions (mol/kg DM intake) were recorded in steers fed the mixed diet. Higher CH 4 emissions (mol/d and mol/kg DM intake) were recorded in steers fed the mixed diet (P, 0·001); the AAx steers produced more CH 4 on a daily basis (mol/d, P, 0·05) but not on a DM intake basis (mol/kg DM intake). Archaea (P¼ 0·002) and protozoa (P,0·001) were found to be more abundant and total bacteria (P,0·001) less abundant (P,0·001) on feeding the mixed diet. The relative abundance of Clostridium cluster IV was found to be greater (P,0·001) and that of cluster XIVa (P¼ 0·025) lower on feeding the mixed diet. The relative abundance of Bacteroides plus Prevotella was greater (P¼ 0·018) and that of Clostridium cluster IV lower (P¼ 0·031) in the LIMx steers. There were no significant relationships between H 2 emissions and microbial abundance. In conclusion, the rate of H 2 production immediately after feeding may lead to transient overloading of methanogenic archaea capacity to use H 2 , resulting in peaks in H 2 emissions from beef cattle.

Microbial communities play critical roles in the gastrointestinal tracts (GIT) of preruminant calves by influencing performance and health. However, little is known about the establishment of microbial communities in the calf GIT or their dynamics during development. In this study, next-generation sequencing was used to assess changes in the bacterial communities of the rumen, jejunum, cecum, and colon in 26 crossbred calves at four developmental stages (7, 28, 49, and 63 days old). Alpha diversity differed among GIT regions with the lowest diversity and evenness in the jejunum, whereas no changes in alpha diversity were observed across developmental stage. Beta diversity analysis showed both region and age effects, with low numbers of operational taxonomic units (OTUs) shared between regions within a given age group or between ages in a given region. Taxonomic analysis revealed that several taxa coexisted in the rumen, jejunum, cecum, and colon but that their abundances differed considerably by GIT region and age. As calves aged, we observed lower abundances of taxa such as ,, and with higher abundances of and in the rumen. The jejunum also displayed taxonomic changes with increases in and taxa in older calves. In the lower gut, taxa such as, , and decreased and S24-7, , and increased as calves aged. These data support a model whereby early and successive colonization by bacteria occurs across the GIT of calves and provides insights into the temporal dynamics of the GIT microbiota of dairy calves during preweaning development. The gastrointestinal tracts (GIT) of ruminants, such as dairy cows, house complex microbial communities that contribute to their overall health and support their ability to produce milk. For example, the rumen microbiota converts feed into usable nutrients, while the jejunal microbiota provides access to protein. Thus, establishing a properly functioning GIT microbiota in dairy calves is critical to their productivity as adult cows. However, little is known about the establishment, maintenance, and dynamics of the calf GIT microbiota in early life. In this study, we evaluated the bacterial communities in the rumen, jejunum, cecum, and colon in dairy calves across preweaning development and show that they are highly variable early on in life before transitioning to a stable community. Understanding the dairy calf GIT microbiota has implications for ensuring proper health during early life and will aid in efforts to develop strategies for improving downstream production.

Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a reach entanglement feature, due to the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss two-qubit thermal entanglement effect on Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements, using this result, we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, such as, the boundary of two entangled regions becomes a disentangled region, this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Despite a similar property had been found for only two-qubit, here we show in the case of a diamond chain structure, which reasonably represents real materials. S i S z J J 0 J Figure 1: (Color Online) Schematic representation of Ising-XYZ chain on diamond structure, σa,i and σ i,b are Heisenberg spins, while Si corresponds to Ising spins.

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An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the T = 0 ground state phase diagram is presented. The phase diagrams have shown to be rather rich, demonstrating large variety of ground states: saturated one, three ferrimagnetic with magnetization equal to 3/5 and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states which could exist at zero magnetic filed. Solving the model exactly within classical transfer-matrix formalism we obtain an exact expressions for all thermodynamic function of the system. The thermodynamic properties of the model have been described exactly by exact calculation of partition function within the direct classical transfer-matrix formalism, the entries of transfer matrix, in their turn, contain the information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of local hamiltonian for vertical link). *