Related papers: Spectral Dimension from Nonlocal Dynamics on Causa…

Starting from certain 3D non-abelian dual systems, we discuss a number of related dual systems in 2D, some of which are obtained by dimensional reduction. The dualities relate massive scalar and vector fields, and may be relevant for string…

We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…

Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…

We follow the dynamics of nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. In the absence of nonlinear terms Anderson localization traps the packet in space. For the nonlinear case a destruction of Anderson…

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ~3/2 at short distance to ~4 at large distance scales, similar to results from…

We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…

This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…

It is shown that the local coupling of a higher dimensional graviton to a closed degenerate two-form produces dimensional reduction by spontaneous breakdown of extra-dimensional translational symmetry. Four dimensional Poincar\'e invariance…

We show that the dimensionful scalar cubic coupling in 3+1 dimensions gives rise to non-decoupling effects and analyze the behavior of these effects. In the process, we clarify how it is perturbatively consistent to construct theories in…

We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a non-universal space-time correlation which depends explicitly on the short-distance properties of disorder, source size,…

We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain…

A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have…

We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…

This paper is devoted to the study of dimension theory, in particular multifractal analysis, for multimodal maps. We describe the Lyapunov spectrum, generalising previous results by Todd. We also study the multifractal spectrum of pointwise…

In the light of some recent results, it is argued that usual concepts of causality and locality are approximations valid at scales greater than the Compton wavelength and corresponding time scales. It follows that the "spooky" non-locality…

We extend Burq's logarithmic decay rate [Bur98] to general compactly supported scatterers in dimension two. The main novelty is using recent results on low-frequency expansions to remove the requirement that the spectrum be regular at zero.…

This work aims at exploring whether the nonlocal correlations due to quantum entanglement could exist without nonlocal causation. This is done with the aid of a toy model to investigate whether the ability of two quantum entangled particles…

We define a nonabelian particle-vortex duality as a $3-$dimensional analogue of the usual $2-$dimensional worldsheet nonabelian T-duality. The transformation is defined in the presence of a global $SU(2)$ symmetry and, although derived from…

We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…