Mean-field theory of baryonic matter for QCD in the large NcN_{c} and heavy quark mass limits

We discuss theoretical issues pertaining to baryonic matter in the combined heavy-quark and large $N_c$ limits of QCD. Witten's classic argument that baryons and interacting systems of baryons can be described in a mean-field approximation with each of the quarks moving in an average potential due to the remaining quarks is heuristic. It is important to justify this heuristic description for the case of baryonic matter since systems of interacting baryons are intrinsically more complicated than single baryons due to the possibility of hidden color states---states in which the subsystems making up the entire baryon crystal are not color-singlet nucleons but rather colorful states coupled together to make a color-singlet state. In this work, we provide a formal justification of this heuristic prescription. In order to do this, we start by taking the heavy quark limit, thus effectively reducing the problem to a many-body quantum mechanical system. This problem can be formulated in terms of integrals over coherent states, which for this problem are simple Slater determinants. We show that for the many-body problem, the support region for these integrals becomes narrow at large $N_c$, yielding an energy which is well-approximated by a single coherent state---that is a mean-field description. Corrections to the energy are of relative order $1/N_c$. While hidden color states are present in the exact state of the heavy quark system, they only influence the interaction energy at sub-leading order in $1/N_{c}$.Comment: 9 page

Study to Assess the Prevalence of Soft Drinking and its Determinants among the School going Children of Gwalior city

Background: Over the time there has been spectrum of changes in the universe. It may be at physical, chemical and cultural level. People have adopted newer life styles like their working style, clothing’s, food habits and so on. One of the pertinent example of this newer food habits is rising consumption of soft drinks rather than traditional home made drinks. This study was aimed to find out various determinants responsible for this rising trend of soft drinking so that effective intervention can be undertaken to overcome this creeping problem. Objectives: To find out the prevalence of soft drinking consumption among the students and to assess the determinants of soft drink consumption among the students. Materials and methods: It was a cross sectional study. A sample of 200 students was selected from the both govt. and private schools by stratified random sampling. Then they all were interviewed by using pre tested, semi structured proforma. Later on data was analyzed manually and by using suitable statistical software. Results: Frequent drinking of soft drinks was found more among the students of private schools than govt. (p < 0.05). A significant association was found between pocket money, TV watching and frequency of soft drinking (p< 0.05).Other reasons which were found to be responsible by far for frequent soft drinking like lack of awareness regarding hazards, frequent TV watching, desire of new taste, lack of health education from the parents side etc. Conclusion: Soft drinking consumption is creeping day by day amongst the children with out knowing their hazards. And they are the future of any country so there should be effective intervention from both sides govt. as well as parents to get rid of it at earliest

Perpendicular magnetic anisotropy in bulk and thin-film CuMnAs for antiferromagnetic memory applications

CuMnAs with perpendicular magnetic anisotropy is proposed as an active material for antiferromagnetic memory. Information can be stored in the antiferromagnetic domain state, while writing and readout can rely on the existence of the surface magnetization. It is predicted, based on first-principles calculations, that easy-axis anisotropy can be achieved in bulk CuMnAs by substituting a few percent of As atoms by Ge, Si, Al, or B. This effect is attributed to the changing occupation of certain electronic bands near the Fermi level induced by the hole doping. The calculated temperature dependence of the magnetic anisotropy does not exhibit any anomalies. Thin CuMnAs(001) films are also predicted to have perpendicular magnetic anisotropy.Comment: 5 pages, 8 figure

Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n >= 3

The long-range interaction of excited neutral atoms has a number of interesting and surprising properties, such as the prevalence of long-range, oscillatory tails, and the emergence of numerically large can der Waals C_6 coefficients. Furthermore, the energetically quasi-degenerate nP states require special attention and lead to mathematical subtleties. Here, we analyze the interaction of excited hydrogen atoms in nS states (3 <= n <= 12) with ground-state hydrogen atoms, and find that the C_6 coefficients roughly grow with the fourth power of the principal quantum number, and can reach values in excess of 240,000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R << a_0/alpha, where a_0 is the Bohr radius and alpha is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a_0/alpha << R << hbar c/L, where L is the Lamb shift energy. In this range, the contribution of quasi-degenerate excited nP states remains nonretarded and competes with the 1/R^2 and 1/R^4 tails of the pole terms which are generated by lower-lying mP states with 2 <= m <= n-1, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range R >> hbar c/L. The familiar 1/R^7 asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation, for highly excited states.Comment: 17 pages; RevTe

Close Examination of the Ground-State Casimir-Polder Interaction: Time-Ordered Versus Covariant Formalism and Radiative Corrections

The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir-Polder interaction using time-ordered perturbation theory, to the matching of the scattering amplitude using quantum electrodynamics. In the first case, a total of twelve time-ordered diagrams need to be considered, while in the second case, one encounters only two Feynman diagrams, namely, the ladder and crossed-ladder contributions. For ground-state interactions, we match the contribution of six of the time-ordered diagrams against the corresponding Feynman diagrams, showing the consistency of the two approaches. Second, we also examine the leading radiative correction to the long-range interaction, which is of relative order O(alpha^3). In doing so, we uncover logarithmic terms, in both the interatomic distance as well as the fine-structure constant, in higher-order corrections to the Casimir-Polder interaction.Comment: 20 pages; IoP article styl

Pressure Shifts in High-Precision Hydrogen Spectroscopy: I. Long-Range Atom-Atom and Atom-Molecule Interactions

We study the theoretical foundations for the pressure shifts in high-precision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P_1/2 and 4P_3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P-2S interaction, where the inclusion of quasi-degenerate 4S-2P_1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasi-degenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R^6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.Comment: 32 pages; 2 figures; this is part 1 of a series of two papers; part 1 carries article number 075005, while part 2 carries article number 075006 in the journal (online journal version has been rectified). arXiv admin note: text overlap with arXiv:1711.1003