Related papers: Discrete scale invariance, and its logarithmic ext…
Unless there is evidence for fractal scaling with a single exponent over distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be questioned. The…
Scale-invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making…
Biroli et al.'s extension of the standard mode-coupling theory to inhomogeneous equilibrium states [Phys. Rev. Lett. 97, 195701 (2006)] allowed them to identify a characteristic length scale that diverges upon approaching the mode-coupling…
In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices,…
The explosion of data on animal behavior in more natural contexts highlights the fact that these behaviors exhibit correlations across many time scales. But there are major challenges in analyzing these data: records of behavior in single…
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
We evaluate the correlation function of the spectral staircase and use it to evaluate the mesoscopic particle number fluctuations in integrable systems.
We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems.
By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory.…
We propose a picture of stock market crashes as critical points in a hierachical system with discrete scaling. The critical exponent is then complex, leading to log-periodic fluctuations in stock market indexes. We present ``experimental''…
The logarithmic slope of the diffractive structure function is a potential observable scanning the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. We report our calculations concerning this quantity, in…
The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit…
There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which…
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex,…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale…
Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is…
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
We revisit the long-standing conjecture that in unitary field theories, scale invariance implies conformality. We explain why the Zamolodchikov-Polchinski proof in D=2 does not work in higher dimensions. We speculate which new ideas might…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…