Related papers: $\alpha$-BS dimension on subsets
Defects in topologically ordered models have interesting properties that are reminiscent of the anyonic excitations of the models themselves. For example, dislocations in the toric code model are known as twists and possess properties that…
We present measurements of the two-dimensional genus of the SDSS-III BOSS catalogs to constrain cosmological parameters governing the shape of the matter power spectrum. The BOSS data are divided into twelve concentric shells over the…
Within the many different models that appeared with the use of cold atoms to design BECs the bubble trap shaped potential has been of great interest. For the anisotropic bubble trap physics in the thin-shell limit the relationship between…
We experimentally study cosmological particle production in a two-dimensional Bose-Einstein condensate, whose density excitations map to an analog cosmology. The expansion of spacetime is realized with tunable interactions. The particle…
We report strong cosmological constraints on the Brans-Dicke (BD) theory of gravity using Cosmic Microwave Background data from Planck.We consider two types of models. First, the initial condition of the scalar field is fixed to give the…
Peres and Solomyak proved that on $\mathbb R^n$, the limits defining the $L^q$-dimension for any $q\in(0,\infty)\setminus\{1\}$, and the entropy dimension of a self-conformal measure exist, without assuming any separation condition. By…
We consider continuous-time (not necessarily finite) Markov chains on discrete spaces and identify a curvature-dimension inequality, the condition $CD_\Upsilon(\kappa,\infty)$, which serves as a natural analogue of the classical…
We numerically determine subleading scaling terms in the ground-state entanglement entropy of several two-dimensional (2D) gapless systems, including a Heisenberg model with N\'eel order, a free Dirac fermion in the {\pi}-flux phase, and…
Let $\beta>1$ be a real number and define the $\beta$-transformation on $[0,1]$ by $T_\beta:x\mapsto \beta x\bmod 1$. Further, define $$W_y(T_{\beta},\Psi):=\{x\in [0, 1]:|T_\beta^nx-y|<\Psi(n) \mbox{ for infinitely many $n$}\}$$ and…
The relative entropy of the massive free bosonic field theory is studied on various compact Riemann surfaces as a universal quantity with physical significance, in particular, for gravitational phenomena. The exact expression for the sphere…
The Bernoulli convolution associated to the real $\beta>1$ and the probability vector $(p_0,..,p_{d-1})$ is a probability measure $\eta_{\beta,p}$ on $\mathbb R$, solution of the self-similarity relation…
We present a holographic method for computing the response of R\'enyi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point…
In this paper we consider two types of dimension that can be defined for products of one-dimensional topologically totally transcendental (t.t.t) structures. The first is topological and considers the interior of projections of the set onto…
We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a…
We introduce dynamic asymptotic dimension, a notion of dimension for actions of discrete groups on locally compact spaces, and more generally for locally compact \'etale groupoids. We study our notion for minimal actions of the integer…
We show that the usual Born-Oppenheimer type of approximation used in quantum gravity, in which a semiclassical time parameter emerges from a weak-coupling expansion of the Wheeler-DeWitt constraint, leads to a unitary theory at least up to…
This paper is an exposition, with some new applications, of our results on the growth of entropy of convolutions. We explain the main result on $\mathbb{R}$, and derive, via a linearization argument, an analogous result for the action of…
Taking into account a fractal structure for the black hole horizon, Barrow argued that the area law of entropy is modified due to quantum-gravitational effects (Barrow in Phys Lett B 808:135643,…
In this paper, we consider spin-3 Chern-Simons-like theories of gravity as extended theories of spin-3 gravity in (2+1)- dimension. In order to determine the number of local degrees of freedom we present the Hamiltonian formulation of these…
It is well-known that $\epsilon$-stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three types of upper metric mean dimensions with potential…