The non-unique Universe

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Godel's incompleteness theorem for theories of everything. Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model

Unitarity and the Bethe-Salpeter Equation

We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $\phi^2\sigma$ interaction Lagrangian and the $\pi N$ system with $s$-, $u$-, and $t$-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in Phys. Rev.

Complex differences in infection rates between ethnic groups in Scotland: a retrospective, national census-linked cohort study of 1.65 million cases

Background Ethnicity can influence susceptibility to infection, as COVID-19 has shown. Few countries have systematically investigated ethnic variations in infection. Methods We linked the Scotland 2001 Census, including ethnic group, to national databases of hospitalizations/deaths and serological diagnoses of bloodborne viruses for 2001–2013. We calculated age-adjusted rate ratios (RRs) in 12 ethnic groups for all infections combined, 15 infection categories, and human immunodeficiency virus (HIV), hepatitis B (HBV) and hepatitis C (HCV) viruses. Results We analysed over 1.65 million infection-related hospitalisations/deaths. Compared with White Scottish, RRs for all infections combined were 0.8 or lower for Other White British, Other White and Chinese males and females, and 1.2–1.4 for Pakistani and African males and females. Adjustment for socioeconomic status or birthplace had little effect. RRs for specific infection categories followed similar patterns with striking exceptions. For HIV, RRs were 136 in African females and 14 in males; for HBV, 125 in Chinese females and 59 in males, 55 in African females and 24 in males; and for HCV, 2.3–3.1 in Pakistanis and Africans. Conclusions Ethnic differences were found in overall rates and many infection categories, suggesting multiple causative pathways. We recommend census linkage as a powerful method for studying the disproportionate impact of COVID-19

Relativistic effects and quasipotential equations

We compare the scattering amplitude resulting from the several quasipotential equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator, Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved numerically without decomposition into partial waves. We analyze both negative-energy state components of the propagators and retardation effects. We found that the scattering solutions of the Spectator and the Equal-Time equations are very close to the nonrelativistic solution even at high energies. The overall relativistic effect increases with the energy. The width of the band for the relative uncertainty in the real part of the scattering $T$ matrix, due to different dynamical equations, is largest for backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.

Graphene based superconducting quantum point contacts

We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentrations of the carriers this monotonic variation acquires a series of peaks. Further analysis of the current-phase relation and the Josephson coupling strength $I_cR_N$ in terms of $W/L$ and the concentration of carriers revels significant differences with those of an ordinary SQPC. On the other hand for a zigzag nanoribbon we find that, similar to an ordinary SQPC, $I_c$ is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.Comment: 8 pages, 5 figure

Detailed electronic structure studies on superconducting MgB2_2 and related compounds

In order to understand the unexpected superconducting behavior of MgB$_2$ compound we have made electronic structure calculations for MgB$_2$ and closely related systems. Our calculated Debye temperature from the elastic properties indicate that the average phonon frequency is very large in MgB$_2$ compared with other superconducting intermetallics and the exceptionally high $T_c$ in this material can be explained through BCS mechanism only if phonon softening occurs or the phonon modes are highly anisotropic. We identified a doubly-degenerate quasi-two dimensional key-energy band in the vicinity of $E_{F}$ along $\Gamma$-A direction of BZ which play an important role in deciding the superconducting behavior of this material. Based on this result, we have searched for similar kinds of electronic feature in a series of isoelectronic compounds such as BeB$_2$, CaB$_2$, SrB$_2$, LiBC and MgB$_2$C$_2$ and found that MgB$_2$C$_2$ is one potential material from the superconductivity point of view. There are contradictory experimental results regarding the anisotropy in the elastic properties of MgB$_2$ ranging from isotropic, moderately anisotropic to highly anisotropic. In order to settle this issue we have calculated the single crystal elastic constants for MgB$_2$ by the accurate full-potential method and derived the directional dependent linear compressibility, Young's modulus, shear modulus and relevant elastic properties. We have observed large anisotropy in the elastic properties. Our calculated polarized optical dielectric tensor shows highly anisotropic behavior even though it possesses isotropic transport property. MgB$_2$ possesses a mixed bonding character and this has been verified from density of states, charge density and crystal orbital Hamiltonian population analyses

Una Visión General del Sistema Financiero Colombiano

Desde finales de los 80 el sistema financiero colombiano ha experimentado cambios sensibles. En efecto, la liberalización financiera, el fortalecimiento de la regulación prudencial, la conversión de un número importante de sociedades en establecimientos de crédito, el aumento en los requisitos de capital, etc. han determinado un cambio de perfil en el sistema. Adicionalmente, en el pasado reciente las autoridades han tomado medidas en cuanto a la estructura de los encajes, aumentos en los requisitos de capital, el acceso al crédito externo, etc. que afectan de manera importante a las entidades financieras. A raíz de estas medidas ha surgido un debate acerca del tipo de sistema financiero que resulta más deseable para Colombia. La discusión es de vital importancia puesto que la estructura de encajes, las formas de intervención del Banco de la República en los mercados cambiario y monetario, la supervisión y todo el aparato regulatorio deben ser consistentes con el tipo de sistema que se desee. Con el fin de contribuir al debate, en este documento se presenta una breve descripción del estado actual del sistema financiero y su evolución reciente, se plantea una reflexión normativa acerca del tipo de sistema financiero que puede resultar más deseable y, finalmente,se presentan algunas recomendaciones.

Genetic predisposition influences plasma lipids of participants on habitual diet, but not the response to reductions in dietary intake of saturated fatty acids

Objective: SNPs identified from genome wide association studies associate with lipid risk markers of cardiovascular disease. This study investigated whether these SNPs altered the plasma lipid response to diet in the ‘RISCK’ study cohort. Methods: Participants (n = 490) from a dietary intervention to lower saturated fat by replacement with carbohydrate or monounsaturated fat, were genotyped for 39 lipid-associated SNPs. The association of each individual SNP, and of the SNPs combined (using genetic predisposition scores), with plasma lipid concentrations was assessed at baseline, and on change in response to 24 weeks on diets. Results: The associations between SNPs and lipid concentrations were directionally consistent with previous findings. The genetic predisposition scores were associated with higher baseline concentrations of plasma total(P = 0.02) and LDL (P = 0.002) cholesterol, triglycerides (P = 0.001) and apolipoprotein B (P = 0.004), and with lower baseline concentrations of HDL cholesterol (P < 0.001) and apolipoprotein A-I (P < 0.001). None of the SNPs showed significant association with the reduction of plasma lipids in response to the dietary interventions and there was no evidence of diet-gene interactions. Conclusion: Results from this exploratory study have shown that increased genetic predisposition was associated with an unfavourable plasma lipid profile at baseline, but did not influence the improvement in lipid profiles by the low-saturated-fat diets

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent $\eta$ has the constant value 1/4, while the exponent $\nu$ runs in a continuous and monotonic way from 1 to $\infty$ (from Ising to O(2)). For N\geq 3 we find a cubic fixed point in the region $u, v \geq 0$, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N=3 we find the exponents $\eta=0.17(8)$ and $\nu=1.3(3)$ at the cubic transition.Comment: 14 pages, 9 figure

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.