A slowly rotating perfect fluid body in an ambient vacuum

A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist solution, and the vacuum region is not asymptotically flat. The impossibility of joining an asymptotically flat vacuum region has been shown in a preceding work.Comment: 7 pages, published versio

The quadrupole moment of slowly rotating fluid balls

In this paper we use the second order formalism of Hartle to study slowly and rigidly rotating stars with focus on the quadrupole moment of the object. The second order field equations for the interior fluid are solved numerically for different classes of possible equations of state and these solutions are then matched to a vacuum solution that includes the general asymptotically flat axisymmetric metric to second order, using the Darmois-Israel procedure. For these solutions we find that the quadrupole moment differs from that of the Kerr metric, as has also been found for some equations of state in other studies. Further we consider the post-Minkowskian limit analytically. In the paper we also illustrate how the relativistic multipole moments can be calculated from a complex gravitational potential.Comment: 13 pages, 5 figure

Variable - temperature scanning optical and force microscope

The implementation of a scanning microscope capable of working in confocal, atomic force and apertureless near field configurations is presented. The microscope is designed to operate in the temperature range 4 - 300 K, using conventional helium flow cryostats. In AFM mode, the distance between the sample and an etched tungsten tip is controlled by a self - sensing piezoelectric tuning fork. The vertical position of both the AFM head and microscope objective can be accurately controlled using piezoelectric coarse approach motors. The scanning is performed using a compact XYZ stage, while the AFM and optical head are kept fixed, allowing scanning probe and optical measurements to be acquired simultaneously and in concert. The free optical axis of the microscope enables both reflection and transmission experiments to be performed.Comment: 24 pages, 9 figures, submitted to the journal "Review of Scientific Instruments

Cognitive Computation sans Representation

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational content is extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing

Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion

A fully explicit renormalized quantum action functional is constructed for the O(N)-model in the auxiliary field formulation at next-to-leading order (NLO) of the 1/N expansion. Counterterms are consistently and explicitly derived for arbitrary constant vacuum expectation value of the scalar and auxiliary fields. The renormalized NLO pion propagator is exact at this order and satisfies Goldstone's theorem. Elimination of the auxiliary field sector at the level of the functional provides with order N^0 accuracy the renormalized effective action of the model in terms of the original variables. Alternative elimination of the pion and sigma propagators provides the renormalized NLO effective potential for the expectation values of the N-vector and of the auxiliary field with the same accuracy.Comment: RevTeX4, 19 pages, 3 figures. Version published Phys. Rev.

Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential

We demonstrate analytically that complex Langevin dynamics can solve the sign problem in one-dimensional QCD in the thermodynamic limit. In particular, it is shown that the contributions from the complex and highly oscillating spectral density of the Dirac operator to the chiral condensate are taken into account correctly. We find an infinite number of classical fixed points of the Langevin flow in the thermodynamic limit. The correct solution originates from a continuum of degenerate distributions in the complexified space.Comment: 20 pages, several eps figures, minor comments added, to appear in JHE

Petrov types of slowly rotating fluid balls

Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the possible Petrov types of various fluid models. It is shown that Petrov type II solutions must reduce to the de Sitter spacetime in the static limit. Two space-times with a physically satisfactory energy-momentum tensor are investigated in detail. For the rotating incompressible fluid, it is proven that the Petrov type cannot be D. The equation of the rotation function $\omega$ can be solved for the Tolman type IV fluid in terms of quadratures. It is also shown that the rotating version of the Tolman IV space-time cannot be Petrov type D.Comment: 14 pages, version to appear in Gen. Rel. Gra

The QCD phase diagram at nonzero quark density

We determine the phase diagram of QCD on the \mu-T plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility. The calculations are carried out on N_t =6,8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+1 flavor staggered fermion action using physical quark masses. After carrying out the continuum extrapolation we find that both quantities result in a similar curvature of the transition line. Furthermore, our results indicate that in leading order the width of the transition region remains essentially the same as the chemical potential is increased.Comment: 12 pages, 6 figure

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, $E_n=\omega_n-i\gamma_n$, satisfying the outgoing radiation condition. For $n\to\infty$, their frequencies $\omega_n$ approach the mass of the vector boson, $M_W$, while their lifetimes $1/\gamma_n$ tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breather-like excitation characterized by pulsations with a frequency approaching $M_W$ and with an amplitude decaying at late times as $t^{-5/6}$.Comment: 4 page

An effective chiral Hadron-Quark Equation of State

We construct an effective model for the QCD equation of state, taking into account chiral symmetry restoration as well as the deconfinement phase transition. The correct asymptotic degrees of freedom at the high and low temperature limits are included (quarks $\leftrightarrow$ hadrons). The model shows a rapid crossover for both order parameters, as is expected from lattice calculations. We then compare the thermodynamic properties of the model at $\mu_B=0$ which turn out to be in qualitative agreement with lattice data, while apparent quantitative differences can be attributed to hadronic contributions and excluded volume corrections. Furthermore we discuss the effects of a repulsive vector type quark interaction at finite baryon number densities on the resulting phase diagram of the model. Our current model is able to reproduce a first-order liquid gas phase transition as expected, but does not show any signs of a first order deconfinement or chiral phase transition. Both transitions rather appear as a very wide crossover in which heavily medium modified hadron coexist with free quarks.Comment: 19 pages, 13 figures Version accepted by J. Phys.