Symmetric Skyrmions

We present candidates for the global minimum energy solitons of charge one to nine in the Skyrme model, generated using sophisticated numerical algorithms. Assuming the Skyrme model accurately represents the low energy limit of QCD, these configurations correspond to the classical nuclear ground states of the light elements. The solitons found are particularly symmetric, for example, the charge seven skyrmion has icosahedral symmetry, and the shapes are shown to fit a remarkable sequence defined by a geometric energy minimization (GEM) rule. We also calculate the energies and sizes to within at least a few percent accuracy. These calculations provide the basis for a future investigation of the low energy vibrational modes of skyrmions and hence the possibility of testing the Skyrme model against experiment.Comment: latex, 9 pages, 1 figure (fig1.gif

Theory of many-fermion systems II: The case of Coulomb interactions

In a recent paper (cond-mat/9703164) a general field-theoretical description of many-fermion systems with short-ranged interactions has been developed. Here we extend this theory to the case of disordered electrons interacting via a Coulomb potential. A detailed discussion is given of the Ward identity that controls the soft modes in the system, and the generalized nonlinear sigma model for the Coulombic case is derived and discussed.Comment: 12 pp., REVTeX, no figs, final version as publishe

Exact Nonperturbative Unitary Amplitudes for 1->N Transitions

I present an extension to arbitrary N of a previously proposed field theoretic model, in which unitary amplitudes for $1->8$ processes were obtained. The Born amplitude in this extension has the behavior $A(1->N)^{tree}\ =\ g^{N-1}\ N!$ expected in a bosonic field theory. Unitarity is violated when $|A(1->N)|>1$, or when $N>\N_crit\simeq e/g.$ Numerical solutions of the coupled Schr\"odinger equations shows that for weak coupling and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}. The very small size of the coefficient 1/\g2 , indicative of a very weak exponential suppression, is not in accord with standard discussions based on saddle point analysis, which give a coefficient $\sim 1.\$ The weak dependence on $N$ could have experimental implications in theories where the exponential suppression is weak (as in this model). Non-perturbative contributions to few-point correlation functions in this theory would arise at order $K\ \simeq\ \left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}$in an expansion in powers of$\g2.$Comment: 11 pages, 3 figures (not included

Correlation functions of higher-dimensional Luttinger liquids

Using higher-dimensional bosonization, we study correlation functions of fermions with singular forward scattering. Following Bares and Wen [Phys. Rev. B 48, 8636 (1993)], we consider density-density interactions in d dimensions that diverge for small momentum transfers as q^{- eta} with eta = 2 (d-1). In this case the single-particle Green's function shows Luttinger liquid behavior. We discuss the momentum distribution and the density of states and show that, in contrast to d=1, in higher dimensions the scaling behavior cannot be characterized by a single anomalous exponent. We also calculate the irreducible polarization for q close to 2 k_F and show that the leading singularities cancel. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.Comment: 7 RevTex pages, 2 figures, minor modifications, to appear in Phys. Rev. B (Feb. 1999

Quasiparticle thermal conductivity in the vortex state of high-Tc_c cuprates

We present the results of a microscopic calculation of the longitudinal thermal conductivity, $\kappa$, of a d-wave superconductor in the mixed state. Our results show an increase in the thermal conductivity with the applied field at low temperatures, and a decrease followed by a nearly field independent $\kappa(H)$ at higher temperatures, in qualitative agreement with the experimental results. We discuss the relationship between the slope of the superconducting gap and the plateau in $\kappa(H)$.Comment: 4 pages, 3 figures, very minor changes to text, published versio

Association of psychological distress, quality of life and costs with carpal tunnel syndrome severity: a crosssectional analysis of the PALMS cohort

Objectives: The PALMS study is designed to identify prognostic factors for outcome from corticosteroid injection and surgical decompression for carpal tunnel syndrome (CTS) and predictors of cost over 2 years. The aim of this paper is to explore the cross-sectional association of baseline patient-reported and clinical severity with anxiety, depression, health-related quality of life and costs of CTS in patients referred to secondary care. Methods: Prospective, multi-centre cohort study initiated in 2013. We collected baseline data on patientreported symptom severity (CTS-6), psychological status (HADS), hand function (Michigan Hand Questionnaire) comorbidities, EQ5D-3L and sociodemographic variables. Nerve conduction tests classified patients into five severity grades (mild to very severe). Data were analysed using a general linear model. Results: 753 patients with CTS provided complete baseline data. Multivariable linear regression adjusting for age, sex, ethnicity, duration of CTS, smoking status, alcohol consumption, employment status, body mass index and comorbidities showed a highly statistically significant relationship between CTS-6 and anxiety, depression and the EQ-5D (p<0.0001 in each case). Likewise, a significant relationship was observed between electrodiagnostic severity and anxiety (p=0.027) but not with depression (p=0.986) or the EQ-5D (p=0.257). NHS and societal costs in the 3 months prior to enrolment were significantly associated with self-reported severity (p<0.0001) but not with electrodiagnostic severity. Conclusions: Patient-reported symptom severity in carpal tunnel syndrome is significantly and positively associated with anxiety, depression, health-related quality of life and NHS and societal costs even when adjusting for age, gender, body mass index, comorbidities, smoking, drinking and occupational status. In contrast there is little or no evidence of any relationship with objectively derived CTS severity. Future research is needed to understand the impact of approaches and treatments that address psychosocial stressors as well as biomedical factors on relief of symptoms from carpal tunnel syndrome.CJH was funded by the National Institute for Health Research (NIHR) through a NIHR Senior Research Fellowship. ECFW is funded by the NIHR Cambridge Biomedical Research Centre

Theory of Fermion Liquids

We develop a general theory of fermion liquids in spatial dimensions greater than one. The principal method, bosonization, is applied to the cases of short and long range longitudinal interactions, and to transverse gauge interactions. All the correlation functions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau Fermi fixed point. Novel fixed points are found, however, in the cases of a super-long range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the 2+1-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction $V({\bf q}) \propto |{\bf q}|^{y-1}$ which controls the density, and hence gauge, fluctuations. For $y < 0$ we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for $y > 0$ the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case $y = 0$ (Coulomb interaction) which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator which is of a marginal Fermi liquid form. Using Ward Identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion, nor vertex corrections, alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also investigate the gauge-invariant density response function. Near momentum $Q = 2 k_F$, in addition to the Kohn anomaly we find singular behavior. In Appendices we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter $f_0 \neq 0$. We also show how Kohn's theorem isComment: Minor corrections and clarifications, and additional references. 30 pages, RevTex 3.0, 3 figures in uuencoded postscript files

Magnetoresistance of composite fermions at \nu=1/2

We have studied temperature dependence of both diagonal and Hall resistivity in the vicinity of $\nu=1/2$. Magnetoresistance was found to be positive and almost independent of temperature: temperature enters resistivity as a logarithmic correction. At the same time, no measurable corrections to the Hall resistivity has been found. Neither of these results can be explained within the mean-field theory of composite fermions by an analogy with conventional low-field interaction theory. There is an indication that interactions of composite fermions with fluctuations of the gauge field may reconcile the theory and experiment.Comment: 9 pages, 4 figure

Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit

Non-Relativistic Fermions Coupled to Transverse Gauge-Fields: The Single-Particle Green's Function in Arbitrary Dimension

We use a bosonization approach to calculate the single-particle Green's function $G ( {\bf{r}} , \tau )$ of non-relativistic fermions coupled to transverse gauge-fields in arbitrary dimension $d$. We find that in $d>3$ transverse gauge-fields do not destroy the Fermi liquid, although for $d < 6$ the quasi-particle damping is anomalously large. For $d \rightarrow 3$ the quasi-particle residue vanishes as $Z \propto \exp [ - \frac{1}{2 \pi ( d-3)} (\frac{ \kappa}{mc } )^2 ]$, where $\kappa$ is the Thomas-Fermi wave-vector, $m$ is the mass of the electrons, and $c$ is the velocity of the gauge-particle. In $d=3$ the system is a Luttinger liquid, with anomalous dimension $\gamma_{\bot} = \frac{1}{6 \pi} ( \frac{ \kappa}{mc} )^2$. For $d < 3$ we find that $G ({\bf{r}} , 0 )$ decays exponentially at large distances.Comment: RevTex, no figures