The Pioneer anomaly: the measure of a topological phase defect of light in cosmology

It is shown that a wave vector representing a light pulse in an adiabatically evolving expanding space should develop, after a round trip (back and forth to the emitter) a geometric phase for helicity states at a given fixed position coordinate of this expanding space.In a section of the Hopf fibration of the Poincare sphere that identifies a projection to the physically allowed states, the evolution defines a parallel transported state that can be joined continuously with the initial state by means of the associated Berry-Pancharatnam connection. The connection allows to compute an anomaly in the frequency for the vector modes in terms of the scale factor of the space-time background being identical to the reported Pioneer Anomaly.Comment: 10 pages, some minor notation changes have been made. Some additional remarks were writte

Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory

We write down the gap equation for the fermion self-energy in a finite-temperature abelian gauge theory in three dimensions. The instantaneous approximation is relaxed, momentum-dependent fermion and photon self-energies are considered, and the corresponding Schwinger-Dyson equation is solved numerically. The relation between the zero-momentum and zero-temperature fermion self-energy and the critical temperature T_c, above which there is no dynamical mass generation, is then studied. We also investigate the effect which the number of fermion flavours N_f has on the results, and we give the phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to appear in Physical Review

Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders

We study systematically the higher order corrections to the parity violating part of the effective action for the Abelian Chern-Simons theory in 2+1 dimensions, using the method of derivative expansion. We explicitly calculate the parity violating parts of the quadratic, cubic and the quartic terms (in fields) of the effective action. We show that each of these actions can be summed, in principle, to all orders in the derivatives. However, such a structure is complicated and not very useful. On the other hand, at every order in the powers of the derivatives, we show that the effective action can also be summed to all orders in the fields. The resulting actions can be expressed in terms of the leading order effective action in the static limit. We prove gauge invariance, both large and small of the resulting effective actions. Various other features of the theory are also brought out.Comment: 36 page

Doubly Bayesian Analysis of Confidence in Perceptual Decision-Making.

Humans stand out from other animals in that they are able to explicitly report on the reliability of their internal operations. This ability, which is known as metacognition, is typically studied by asking people to report their confidence in the correctness of some decision. However, the computations underlying confidence reports remain unclear. In this paper, we present a fully Bayesian method for directly comparing models of confidence. Using a visual two-interval forced-choice task, we tested whether confidence reports reflect heuristic computations (e.g. the magnitude of sensory data) or Bayes optimal ones (i.e. how likely a decision is to be correct given the sensory data). In a standard design in which subjects were first asked to make a decision, and only then gave their confidence, subjects were mostly Bayes optimal. In contrast, in a less-commonly used design in which subjects indicated their confidence and decision simultaneously, they were roughly equally likely to use the Bayes optimal strategy or to use a heuristic but suboptimal strategy. Our results suggest that, while people's confidence reports can reflect Bayes optimal computations, even a small unusual twist or additional element of complexity can prevent optimality

On the Derivative Expansion at Finite Temperature

In this short note, we indicate the origin of nonanalyticity in the method of derivative expansion at finite temperature and discuss some of its consequences.Comment: 7 pages, UR-1363, ER40685-81

Effective Lagrangians for BCS Superconductors at T=0

We show that the low frequency, long wavelength dynamics of the phase of the pair field for a BCS-type s-wave superconductor at T=0 is equivalent to that of a time-dependent non-linear Schr\"odinger Lagrangian (TDNLSL), when terms required by Galilean invariance are included. If the modulus of the pair field is also allowed to vary, the system is equivalent to two coupled TDNLSL's. We also refer the interested reader to our earlier paper, `Nonlinear Schrodinger equation for superconductors' [cond-mat/9312099], for a different line of derivationComment: Latex, 13 page

Simcluster: clustering enumeration gene expression data on the simplex space

Transcript enumeration methods such as SAGE, MPSS, and sequencing-by-synthesis EST "digital northern", are important high-throughput techniques for digital gene expression measurement. As other counting or voting processes, these measurements constitute compositional data exhibiting properties particular to the simplex space where the summation of the components is constrained. These properties are not present on regular Euclidean spaces, on which hybridization-based microarray data is often modeled. Therefore, pattern recognition methods commonly used for microarray data analysis may be non-informative for the data generated by transcript enumeration techniques since they ignore certain fundamental properties of this space.

Here we present a software tool, Simcluster, designed to perform clustering analysis for data on the simplex space. We present Simcluster as a stand-alone command-line C package and as a user-friendly on-line tool. Both versions are available at: http://xerad.systemsbiology.net/simcluster.

Simcluster is designed in accordance with a well-established mathematical framework for compositional data analysis, which provides principled procedures for dealing with the simplex space, and is thus applicable in a number of contexts, including enumeration-based gene expression data

The low-energy phase-only action in a superconductor: a comparison with the XY model

The derivation of the effective theory for the phase degrees of freedom in a superconductor is still, to some extent, an open issue. It is commonly assumed that the classical XY model and its quantum generalizations can be exploited as effective phase-only models. In the quantum regime, however, this assumption leads to spurious results, such as the violation of the Galilean invariance in the continuum model. Starting from a general microscopic model, in this paper we explicitly derive the effective low-energy theory for the phase, up to fourth-order terms. This expansion allows us to properly take into account dynamic effects beyond the Gaussian level, both in the continuum and in the lattice model. After evaluating the one-loop correction to the superfluid density we critically discuss the qualitative and quantitative differences between the results obtained within the quantum XY model and within the correct low-energy theory, both in the case of s-wave and d-wave symmetry of the superconducting order parameter. Specifically, we find dynamic anharmonic vertices, which are absent in the quantum XY model, and are crucial to restore Galilean invariance in the continuum model. As far as the more realistic lattice model is concerned, in the weak-to-intermediate-coupling regime we find that the phase-fluctuation effects are quantitatively reduced with respect to the XY model. On the other hand, in the strong-coupling regime we show that the correspondence between the microscopically derived action and the quantum XY model is recovered, except for the low-density regime.Comment: 29 pages, 11 figures. Slightly revised presentation, accepted for publication in Phys. Rev.

Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective ``phase only'' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility $S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only in dirty systems. On the other hand, our analytical results support the statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in d-wave superconductors the CG mode can exist in clean systems down to the much lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results.Comment: 23 pages, RevTeX4, 12 EPS figures; final version to appear in PR

Deviations from Fermi-Liquid behaviour in (2+1)-dimensional Quantum Electrodynamics and the normal phase of high-TcT_c Superconductors

We argue that the gauge-fermion interaction in multiflavour quantum electrodynamics in $(2 + 1)$-dimensions is responsible for non-fermi liquid behaviour in the infrared, in the sense of leading to the existence of a non-trivial (quasi) fixed point that lies between the trivial fixed point (at infinite momenta) and the region where dynamical symmetry breaking and mass generation occurs. This quasi-fixed point structure implies slowly varying, rather than fixed, couplings in the intermediate regime of momenta, a situation which resembles that of (four-dimensional) `walking technicolour' models of particle physics. The inclusion of wave-function renormalization yields marginal $O(1/N)$-corrections to the `bulk' non-fermi liquid behaviour caused by the gauge interaction in the limit of infinite flavour number. Such corrections lead to the appearance of modified critical exponents. In particular, at low temperatures there appear to be logarithmic scaling violations of the linear resistivity of the system of order $O(1/N)$. Connection with the anomalous normal-state properties of certain condensed matter systems relevant for high-temperature superconductivity is briefly discussed. The relevance of the large (flavour) $N$ expansion to the fermi-liquid problem is emphasized. As a partial result of our analysis, we point out the absence of Charge-Density-Wave Instabilities from the effective low-energy theory, as a consequence of gauge invariance.Comment: Latex file, 35 pages, Two figures not included, available upon reques