Bosonization in the two-channel Kondo model

The bosonization of the $S=1/2$ anisotropic two-channel Kondo model is shown to yield two equivalent representations of the original problem. In a straight forward extension of the Emery-Kivelson approach, the interacting resonant level model previously derived by the Anderson-Yuval technique is obtained. In addition, however, a ``($\sigma$,$\tau$)'' description is also found. The strong coupling fixed point of the ($\sigma$,$\tau$) model was originally postulated to be related to the intermediate coupling fixed point of the two-channel Kondo model. The equivalence of the $\sigma$,$\tau$ model to the two-channel Kondo model is formally established. A summary of what one may learn from a simple study of these different representations is also given.Comment: 5 pages, latex (uses revtex and epsf macros) with 1 postscript figur

The prevalence of loneliness across 113 countries: systematic review and meta-analysis.

OBJECTIVES: To identify data availability, gaps, and patterns for population level prevalence of loneliness globally, to summarise prevalence estimates within World Health Organization regions when feasible through meta-analysis, and to examine temporal trends of loneliness in countries where data exist. DESIGN: Systematic review and meta-analysis. DATA SOURCES: Embase, Medline, PsycINFO, and Scopus for peer reviewed literature, and Google Scholar and Open Grey for grey literature, supplemented by backward reference searching (to 1 September 2021) ELIGIBILITY CRITERIA FOR SELECTING STUDIES: Observational studies based on nationally representative samples (n≥292), validated instruments, and prevalence data for 2000-19. Two researchers independently extracted data and assessed the risk of bias using the Joanna Briggs Institute checklist. Random effects meta-analysis was conducted in the subset of studies with relatively homogeneous research methods by measurement instrument, age group, and WHO region. RESULTS: Prevalence data were available for 113 countries or territories, according to official WHO nomenclature for regions, from 57 studies. Data were available for adolescents (12-17 years) in 77 countries or territories, young adults (18-29 years) in 30 countries, middle aged adults (30-59 years) in 32 countries, and older adults (≥60 years) in 40 countries. Data for all age groups except adolescents were lacking outside of Europe. Overall, 212 estimates for 106 countries from 24 studies were included in meta-analyses. The pooled prevalence of loneliness for adolescents ranged from 9.2% (95% confidence interval 6.8% to 12.4%) in South-East Asia to 14.4% (12.2% to 17.1%) in the Eastern Mediterranean region. For adults, meta-analysis was conducted for the European region only, and a consistent geographical pattern was shown for all adult age groups. The lowest prevalence of loneliness was consistently observed in northern European countries (2.9%, 1.8% to 4.5% for young adults; 2.7%, 2.4% to 3.0% for middle aged adults; and 5.2%, 4.2% to 6.5% for older adults) and the highest in eastern European countries (7.5%, 5.9% to 9.4% for young adults; 9.6%, 7.7% to 12.0% for middle aged adults; and 21.3%, 18.7% to 24.2% for older adults). CONCLUSION: Problematic levels of loneliness are experienced by a substantial proportion of the population in many countries. The substantial difference in data coverage between high income countries (particularly Europe) and low and middle income countries raised an important equity issue. Evidence on the temporal trends of loneliness is insufficient. The findings of this meta-analysis are limited by data scarcity and methodological heterogeneity. Loneliness should be incorporated into general health surveillance with broader geographical and age coverage, using standardised and validated measurement tools. SYSTEMATIC REVIEW REGISTRATION: PROSPERO CRD42019131448

Renormalization Group and Fermi Liquid Theory

We give a Hamiltonian based interpretation of microscopic Fermi liquid theory within a renormalization group framework. We identify the fixed point Hamiltonian of Fermi liquid theory, with the leading order corrections, and show that this Hamiltonian in mean field theory gives the Landau phenomenological theory. A renormalized perturbation theory is developed for calculations beyond the Fermi liquid regime. We also briefly discuss the breakdown of Fermi liquid theory as it occurs in the Luttinger model, and the infinite dimensional Hubbard model at the Mott transition.Comment: 37 pages, postscript, Imperial College preprint 1994. Latex file plus separate figures available on reques

Flux flow resistivity and vortex viscosity of high-Tc films

The flux flow regime of high-T$_{\rm c}$ samples of different normal state resistivities is studied in the temperature range where the sign of the Hall effect is reversed. The scaling of the vortex viscosity with normal state resistivity is consistent with the Bardeen-Stephen theory. Estimates of the influence of possible mechanisms suggested for the sign reversal of the Hall effect are also given.Comment: 3 pages. 4 figures upon reques

Extended bound states and resonances of two fermions on a periodic lattice

The high-$T_c$ cuprates are possible candidates for d-wave superconductivity, with the Cooper pair wave function belonging to a non-trivial irreducible representation of the lattice point group. We argue that this d-wave symmetry is related to a special form of the fermionic kinetic energy and does not require any novel pairing mechanism. In this context, we present a detailed study of the bound states and resonances formed by two lattice fermions interacting via a non-retarded potential that is attractive for nearest neighbors but repulsive for other relative positions. In the case of strong binding, a pair formed by fermions on adjacent lattice sites can have a small effective mass, thereby implying a high condensation temperature. For a weakly bound state, a pair with non-trivial symmetry tends to be smaller in size than an s-wave pair. These and other findings are discussed in connection with the properties of high-$T_c$ cuprate superconductors.Comment: 21 pages, RevTeX, 4 Postscript figures, arithmetic errors corrected. An abbreviated version (no appendix) appeared in PRB on March 1, 199

Entanglement transfer from dissociated molecules to photons

We introduce and study the concept of a reversible transfer of the quantum state of two internally-translationally entangled fragments, formed by molecular dissociation, to a photon pair. The transfer is based on intracavity stimulated Raman adiabatic passage and it requires a combination of processes whose principles are well established.Comment: 5 pages, 3 figure

Exclusion statistics for fractional quantum Hall states on a sphere

We discuss exclusion statistics parameters for quasiholes and quasielectrons excited above the fractional quantum Hall states near $\nu=p/(2np+1)$. We derive the diagonal statistics parameters from the (``unprojected'') composite fermion (CF) picture. We propose values for the off-diagonal (mutual) statistics parameters as a simple modification of those obtained from the unprojected CF picture, by analyzing finite system numerical spectra in the spherical geometry.Comment: 9 pages, Revtex, 4 Postscript figures. Universality of the statistics parameters is stressed, 2 figs adde

Two-Channel Kondo Physics from Tunnelling Impurities with Triangular Symmetry

Tunnelling impurities in metals have been known for some time to have the potential for exhibiting Kondo-like physics. However previous models based on an impurity hopping between two equivalent positions have run into trouble due to the existence of relevant operators that drive the system away from the non-Fermi-liquid Kondo fixed point. In the case of an impurity hopping among positions with higher symmetry, such as triangular symmetry, it is shown here that the non-Fermi-liquid behavior at low temperatures can be generic. Using various bosonization techniques, the fixed point is shown to be {\em stable}. However, unlike the conventional two-channel Kondo (2CK) model, it has {\em four} leading irrelevant operators, implying that while the form of the singular temperature dependence of physical quantities is similar to the 2CK model, there will not be simple universal amplitude ratios. The phase diagram of this system is analyzed and a critical manifold is found to separate the non-Fermi-liquid from a conventional Fermi liquid fixed point. Generalization to higher symmetries, such as cubic, and the possibility of physical realizations with dynamic Jahn-Teller impurities is discussed.Comment: 20 pages, 4 figures, RevTex format, submitted to Phys. Rev.