Renormalization Group Analysis of a Quivering String Model of Posture Control

Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various non-trivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak non-linearities is confirmed. Correlations in posture fluctuations are obtained in both the time and space domain. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both the large-separation (along the string) and long-time regimes of posture control.Comment: 20 pages, 13 figures, RevTeX, accepted for publication in PR

No realistic wormholes from ghost-free scalar-tensor phantom dark energy

It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(\Phi)$ is everywhere positive and the scalar field $\Phi$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(\Phi)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions require severe fine tuning and a very peculiar kind of model. If $f < 0$ is allowed, it is argued (and confirmed by previous investigations) that such solutions are generically unstable under non-static perturbations, the instability appearing right near transition surfaces to negative $f$.Comment: 8 pages, late

Classical and semi-classical energy conditions

The standard energy conditions of classical general relativity are (mostly) linear in the stress-energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically non-linear in the stress-energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this article we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking--Ellis type I, II, III, and IV classification of stress-energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included.Comment: V1: 25 pages. Draft chapter, on which the related chapter of the book "Wormholes, Warp Drives and Energy Conditions" (to be published by Springer), will be based. V2: typos fixed. V3: small typo fixe

Jerk, snap, and the cosmological equation of state

Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. In particular, the value and derivatives of the scale factor determined at the current epoch place constraints on the value and derivatives of the cosmological equation of state at the current epoch. Determining the first three Taylor coefficients of the equation of state at the current epoch requires a measurement of the deceleration, jerk, and snap -- the second, third, and fourth derivatives of the scale factor with respect to time. Higher-order Taylor coefficients in the equation of state are related to higher-order time derivatives of the scale factor. Since the jerk and snap are rather difficult to measure, being related to the third and fourth terms in the Taylor series expansion of the Hubble law, it becomes clear why direct observational constraints on the cosmological equation of state are so relatively weak; and are likely to remain weak for the foreseeable future.Comment: V1: 10 pages; uses iopart.cls setstack.sty V2: six additional references, some clarifying comments and discussion, no physics changes. V3: significant additions based on community feedback; explicit calculations now carried out to fourth order in redshift. V4: Discussion of current observational situation added. This version accepted for publication in Classical and Quantum Gravity. Now 15 page

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long and short-wavelength modes of the field. The field model considered consists of a scalar field of mass $M$ with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behaviour is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size $M^{-1}$. This effect makes a substantial contribution to the total decay rate.Comment: 27 pages, RevTeX, 1 figure (uses epsf.sty

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long and short-wavelength modes of the field. The field model considered consists of a scalar field of mass $M$ with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behaviour is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size $M^{-1}$. This effect makes a substantial contribution to the total decay rate.Comment: 27 pages, RevTeX, 1 figure (uses epsf.sty

Scalar-mediated ttˉt\bar t forward-backward asymmetry

A large forward-backward asymmetry in $t\bar t$ production, for large invariant mass of the $t\bar t$ system, has been recently observed by the CDF collaboration. Among the scalar mediated mechanisms that can explain such a large asymmetry, only the t-channel exchange of a color-singlet weak-doublet scalar is consistent with both differential and integrated $t\bar t$ cross section measurements. Constraints from flavor changing processes dictate a very specific structure for the Yukawa couplings of such a new scalar. No sizable deviation in the differential or integrated $t\bar t$ production cross section is expected at the LHC.Comment: 22 pages, 1 figure and 2 tables. v2: Corrected Eqs.(50,51,74), adapted Fig.1, Tab.1 and relevant discussions. Extended discussion of top decay and single to

Rare B decays and Tevatron top-pair asymmetry

The recent Tevatron result on the top quark forward-backward asymmetry, which deviates from its standard model prediction by 3.4$\sigma$, has prompted many authors to build new models to account for this anomaly. Among the various proposals, we find that those mechanisms which produce $t\bar t$ via $t$- or $u$-channel can have a strong correlation to the rare B decays. We demonstrate this link by studying a model with a new charged gauge boson, $W'$. In terms of the current measurements on $B\to \pi K$ decays, we conclude that the branching ratio for $B^-\to \pi^- \bar K^0$ is affected most by the new effects. Furthermore, using the world average branching ratio for the exclusive B decays at $2\sigma$ level, we discuss the allowed values for the new parameters. Finally, we point out that the influence of the new physics effects on the direct CP asymmetry in B decays is insignificant.Comment: 15 page, 6 figures, typos corrected and references added, final version to appear journa

Match-action: the role of motion and audio in creating global change blindness in film

An everyday example of change blindness is our difficulty to detect cuts in an edited moving-image. Edit Blindness (Smith & Henderson, 2008) is created by adhering to the continuity editing conventions of Hollywood, e.g. coinciding a cut with a sudden onset of motion (Match-Action). In this study we isolated the roles motion and audio play in limiting awareness of match-action cuts by removing motion before and/or after cuts in existing Hollywood film clips and presenting the clips with or without the original soundtrack whilst participants tried to detect cuts. Removing post-cut motion significantly decreased cut detection time and the probability of missing the cut. By comparison, removing pre-cut motion had no effect suggesting, contrary to the editing literature, that the onset of motion before a cut may not be as critical for creating edit blindness as the motion after a cut. Analysis of eye movements indicated that viewers reoriented less to new content across intact match-action cuts than shots with motion removed. Audio played a surprisingly large part in creating edit blindness with edit blindness mostly disappearing without audio. These results extend film editor intuitions and are discussed in the context of the Attentional Theory of Cinematic Continuity (Smith, 2012a)