Lattice Gauge Fixing as Quenching and the Violation of Spectral Positivity

Lattice Landau gauge and other related lattice gauge fixing schemes are known to violate spectral positivity. The most direct sign of the violation is the rise of the effective mass as a function of distance. The origin of this phenomenon lies in the quenched character of the auxiliary field $g$ used to implement lattice gauge fixing, and is similar to quenched QCD in this respect. This is best studied using the PJLZ formalism, leading to a class of covariant gauges similar to the one-parameter class of covariant gauges commonly used in continuum gauge theories. Soluble models are used to illustrate the origin of the violation of spectral positivity. The phase diagram of the lattice theory, as a function of the gauge coupling $\beta$ and the gauge-fixing parameter $\alpha$, is similar to that of the unquenched theory, a Higgs model of a type first studied by Fradkin and Shenker. The gluon propagator is interpreted as yielding bound states in the confined phase, and a mixture of fundamental particles in the Higgs phase, but lattice simulation shows the two phases are connected. Gauge field propagators from the simulation of an SU(2) lattice gauge theory on a $20^4$ lattice are well described by a quenched mass-mixing model. The mass of the lightest state, which we interpret as the gluon mass, appears to be independent of $\alpha$ for sufficiently large $\alpha$.Comment: 28 pages, 14 figures, RevTeX

Chiral extrapolation of lattice data for B-meson decay constant

The B-meson decay constant fB has been calculated from unquenched lattice QCD in the unphysical region. For extrapolating the lattice data to the physical region, we propose a phenomenological functional form based on the effective chiral perturbation theory for heavy mesons, which respects both the heavy quark symmetry and the chiral symmetry, and the non-relativistic constituent quark model which is valid at large pion masses. The inclusion of pion loop corrections leads to nonanalytic contributions to fB when the pion mass is small. The finite-range regularization technique is employed for the resummation of higher order terms of the chiral expansion. We also take into account the finite volume effects in lattice simulations. The dependence on the parameters and other uncertainties in our model are discussed.Comment: 11 pages, 3 Postscript figures, accepted for publication in EPJ

Quantum tunneling in a three dimensional network of exchange coupled single-molecule magnets

A Mn4 single-molecule magnet (SMM) is used to show that quantum tunneling of magnetization (QTM) is not suppressed by moderate three dimensional exchange coupling between molecules. Instead, it leads to an exchange bias of the quantum resonances which allows precise measurements of the effective exchange coupling that is mainly due to weak intermolecular hydrogen bounds. The magnetization versus applied field was recorded on single crystals of [Mn4]2 using an array of micro-SQUIDs. The step fine structure was studied via minor hysteresis loops.Comment: 4 pages, 4 figure

Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

Novel anisotropy in the superconducting gap structure of Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} probed by quasiparticle heat transport

Since the nature of pairing interactions is manifested in the superconducting gap symmetry, the exact gap structure, particularly any deviation from the simple d_{x^2-y^2} symmetry, would help elucidating the pairing mechanism in high-T_c cuprates. Anisotropic heat transport measurement in Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} (Bi-2212) reveals that the quasiparticle populations are different for the two nodal directions and thus the gap structure must be uniquely anisotropic, suggesting that pairing is governed by interactions with a rather complicated anisotropy. Intriguingly, it is found that the "plateau" in the magnetic-field dependence of the thermal conductivity is observed only in the b-axis transport.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let

Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Evidence for field-induced excitations in low-temperature thermal conductivity of Bi_2Sr_2CaCu_2O_8

The thermal conductivity ,$\kappa$, of Bi_2Sr_2CaCu_2O_8 was studied as a function of magnetic field. Above 5 K, after an initial decrease, $\kappa(H)$ presents a kink followed by a plateau, as recently reported by Krishana et al.. By contrast, below 1K, the thermal conductivity was found to \emph{increase} with increasing field. This behavior is indicative of a finite density of states and is not compatible with the existence of a field-induced fully gapped $d_{x^{2}-y^{2}}+id_{xy}$ state which was recently proposed to describe the plateau regime. Our low-temperature results are in agreement with recent works predicting a field-induced enhancement of thermal conductivity by Doppler shift of quasi-particle spectrum.Comment: 4 pages including 4 eps figures, submitted to Phys. Rev. Let

Angle Dependence of the Transverse Thermal Conductivity in YBa2_2Cu3_3O7_7 single crystals: Doppler Effect vs. Andreev scattering

We have measured the transverse thermal conductivity $\kappa_{xy}$ of twinned and untwinned YBa$_2$Cu$_3$O$_7$ single crystals as a function of angle $\theta$ between the magnetic field applied parallel to the CuO$_2$ planes and the heat current direction, at different magnetic fields and temperatures. For both crystals we observed a clear twofold variation in the field-angle dependence of $\kappa_{xy}(\theta) = - \kappa^0_{xy}(T,B) \sin(2\theta)$. We have found that the oscillation amplitude $\kappa^0_{xy}$ depends on temperature and magnetic field. Our results show that $\kappa^0_{xy} = a B \ln(1/(bB))$ with the temperature- and sample-dependent parameters $a$ and $b$. We discuss our results in terms of Andreev scattering of quasiparticles by vortices and a recently proposed theory based on the Doppler shift in the quasiparticle spectrum.Comment: 5 pages, 4 figure

Stability of complex hyperbolic space under curvature-normalized Ricci flow

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result, we also define suitably weighted little H\"{o}lder spaces on a complete noncompact manifold and establish their interpolation properties.Comment: Some typos in version 2 are correcte