The pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau Theory

It is well known that conventional pairing fluctuation theory at the Hartree level leads to a normal state pseudogap in the fermionic spectrum. Our goal is to extend this Hartree approximated scheme to arrive at a generalized mean field theory of pseudogapped superconductors for all temperatures $T$. While an equivalent approach to the pseudogap has been derived elsewhere using a more formal Green's function decoupling scheme, in this paper we re-interpret this mean field theory and BCS theory as well, and demonstrate how they naturally relate to ideal Bose gas condensation. Here we recast the Hartree approximated Ginzburg-Landau self consistent equations in a T-matrix form. This recasting makes it possible to consider arbitrarily strong attractive coupling, where bosonic degrees of freedom appear at $T^*$ considerably above $T_c$. The implications for transport both above and below $T_c$ are discussed. Below $T_c$ we find two types of contributions. Those associated with fermionic excitations have the usual BCS functional form. That they depend on the magnitude of the excitation gap, nevertheless, leads to rather atypical transport properties in the strong coupling limit, where this gap (as distinct from the order parameter) is virtually $T$-independent. In addition, there are bosonic terms arising from non-condensed pairs whose transport properties are shown here to be reasonably well described by an effective time-dependent Ginzburg-Landau theory.Comment: 14 pages, 5 figures, REVTeX4, submitted to PRB; clarification of the diagrammatic technique added, one figure update

Unconventional Pairing in Heavy Fermion Metals

The Fermi-liquid theory of superconductivity is applicable to a broad range of systems that are candidates for unconventional pairing. Fundamental differences between unconventional and conventional anisotropic superconductors are illustrated by the unique effects that impurities have on the low-temperature transport properties of unconventional superconductors. For special classes of unconventional superconductors the low-temperature transport coefficients are {\it universal}, i.e. independent of the impurity concentration and scattering phase shift. The existence of a universal limit depends on the symmetry of the order parameter and is achieved at low temperatures $k_B T \ll \gamma \ll \Delta_0$, where $\gamma$ is the bandwidth of the impurity induced Andreev bound states. In the case of UPt$_3$ thermal conductivity measurements favor an $E_{1g}$ or $E_{2u}$ ground state. Measurements at ultra-low temperatures should distinguish different pairing states.Comment: 8 pages in a LaTex (3.0) file plus 5 Figures in PostScript. To appear in the Proceedings of the XXI International Conference on Low Temperature Physics held in Prague, 8-14 August 199

Superconducting transitions from the pseudogap state: d-wave symmetry, lattice, and low-dimensional effects

We investigate the behavior of the superconducting transition temperature within a previously developed BCS-Bose Einstein crossover picture. This picture, based on a decoupling scheme of Kadanoff and Martin, further extended by Patton, can be used to derive a simple form for the superconducting transition temperature in the presence of a pseudogap. We extend previous work which addressed the case of s-wave pairing in jellium, to explore the solutions for T_c as a function of variable coupling in more physically relevant situations. We thereby ascertain the effects of reduced dimensionality, periodic lattices and a d-wave pairing interaction. Implications for the cuprate superconductors are discussed.Comment: REVTeX, 11 pages, 6 EPS figures included, Replace with published versio

Associations of Problematic Internet Use, Weight-Related Self-Stigma, and Nomophobia with Physical Activity: Findings from Mainland China, Taiwan, and Malaysia

Insufficient physical activity is a common problem for university students because they may engage in sedentary lifestyle owing to excessive time spent on their smartphones and social media use. This may result in problematic internet use (PIU) and nomophobia (fear of not having a mobile phone). Moreover, prior evidence shows that weight-related self-stigma is an important factor contributing to low physical activity. Therefore, the present study examined the associations between PIU, nomophobia, and physical activity among university students across mainland China, Taiwan, and Malaysia. Participants (3135 mainland Chinese, 600 Taiwanese, and 622 Malaysian) completed the Bergen Social Media Addiction Scale (BSMAS), Smartphone Application-Based Addiction Scale (SABAS), Nomophobia Questionnaire (NMPQ), Weight Self-Stigma Questionnaire (WSSQ), and International Physical Activity Questionnaire Short Form (IPAQ-SF). The measurement invariance of the assessed questionnaires was supported across the three regions. The present findings analyzed using partial least squares structural equation modeling showed that (i) greater nomophobia was associated with higher levels of physical activity, (ii) greater weight-related self-stigma was associated with higher levels of physical activity, and (iii) greater nomophobia was associated with greater weight-related self-stigma. Although the present findings suggest the possibility that experiencing some level of nomophobia or weight-related self-stigma appears to help improve physical activity, it is not recommended that these be encouraged, but reducing PIU should be targeted as a means to improve physical activit

Free Energy of an Inhomogeneous Superconductor: a Wave Function Approach

A new method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based on the quasiclassical limit (or Andreev approximation) of the Bogoliubov-de Gennes (or wave function) formulation of the theory of weakly coupled superconductors. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. We find that both the local density of states and the free energy density of an inhomogeneous superconductor can be expressed in terms of the diagonal resolvent of the corresponding Andreev Hamiltonian, resolvent which obeys the so-called Gelfand-Dikii equation. Also, the connection between the well known Eilenberger equation for the quasiclassical Green's function and the less known Gelfand-Dikii equation for the diagonal resolvent of the Andreev Hamiltonian is established. These results are used to construct a general algorithm for calculating the (gauge invariant) gradient expansion of the free energy density of an inhomogeneous superconductor at arbitrary temperatures.Comment: REVTeX, 28 page

Identification of the Orbital Pairing Symmetry in UPt_3

This paper summarizes the results of a comprehensive analysis of the thermodynamic and transport data for the superconducting phases of UPt_3. Calculations of the transverse sound attenuation as a function of temperature, frequency, polarization, and disorder are presented for the leading models of the superconducting order parameter. Measurements of the specific heat, thermal conductivity, and transverse sound attenuation place strong constraints on the orbital symmetry of the superconducting order parameter. We show that the superconducting A and B phases are in excellent agreement with pairing states belonging to the odd-parity E_{2u} orbital representation.Comment: 11 pages with 7 figure

Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective

Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.Comment: 54 pages, 37 figures, review written for EPJA and APPN; one parag. added end of section 3.4, and one at the end of section 3.2.2; some Refs. added, and some other minor change

Pairing fluctuations and pseudogaps in the attractive Hubbard model

The two-dimensional attractive Hubbard model is studied in the weak to intermediate coupling regime by employing a non-perturbative approach. It is first shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T*, also in good agreement with quantum Monte Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classical regime $\omega < T$ of the two-dimensional system. With increasing temperature the spectral weight fills in the pseudogap instead of closing it and the pseudogap appears earlier in the density of states than in the spectral function. Small temperature changes around T* can modify the spectral weight over frequency scales much larger than temperature. Several qualitative results for the s-wave case should remain true for d-wave superconductors.Comment: 20 pages, 12 figure

Comparative Studies in the A30P and A53T α-Synuclein C. elegans Strains to Investigate the Molecular Origins of Parkinson's Disease

The aggregation of α-synuclein is a hallmark of Parkinson's disease (PD) and a variety of related neurological disorders. A number of mutations in this protein, including A30P and A53T, are associated with familial forms of the disease. Patients carrying the A30P mutation typically exhibit a similar age of onset and symptoms as sporadic PD, while those carrying the A53T mutation generally have an earlier age of onset and an accelerated progression. We report two C. elegans models of PD (PDA30P and PDA53T), which express these mutational variants in the muscle cells, and probed their behavior relative to animals expressing the wild-type protein (PDWT). PDA30P worms showed a reduced speed of movement and an increased paralysis rate, control worms, but no change in the frequency of body bends. By contrast, in PDA53T worms both speed and frequency of body bends were significantly decreased, and paralysis rate was increased. α-Synuclein was also observed to be less well localized into aggregates in PDA30P worms compared to PDA53T and PDWT worms, and amyloid-like features were evident later in the life of the animals, despite comparable levels of expression of α-synuclein. Furthermore, squalamine, a natural product currently in clinical trials for treating symptomatic aspects of PD, was found to reduce significantly the aggregation of α-synuclein and its associated toxicity in PDA53T and PDWT worms, but had less marked effects in PDA30P. In addition, using an antibody that targets the N-terminal region of α-synuclein, we observed a suppression of toxicity in PDA30P, PDA53T and PDWT worms. These results illustrate the use of these two C. elegans models in fundamental and applied PD research