Related papers: $\alpha$-BS dimension on subsets
In this paper we study the topology of a set naturally arising from the study of $\beta$-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and…
Both the Barrow and Tsallis $\delta$ entropies are one-parameter generalizations of the black-hole entropy, with the same microcanonical functional form. The ensuing deformation is quantified by a dimensionless parameter $\Delta$, which in…
The purpose of this note is to record a consequence, for general metric spaces, of a recent result of David Bate. We prove the following fact: Let $X$ be a compact metric space of topological dimension $n$. Suppose that the $n$-dimensional…
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been…
Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions…
We study the asymptotic laws for the number, Betti numbers, and isotopy classes of connected components of zero sets of real Gaussian random fields, where the random zero sets almost surely consist of submanifolds of codimension greater…
Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of…
We use exact Quantum Monte Carlo techniques to study the properties of quantum droplets in two-component bosonic mixtures with contact interactions in one spatial dimension. We systematically study the surface tension, the density profile…
We present a simple gedanken experiment in which a compact object traverses a spacetime with three macroscopic spatial dimensions and $n$ compact dimensions. The compactification radius is allowed to vary, as a function of the object's…
We present a systematic investigation of the thermodynamic topology for a broad class of asymptotically charged Anti-de Sitter (AdS) black holes in Einstein-Maxwell-Dilaton (EMD) theories, examining how scalar coupling parameters and…
We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report…
Follow-up comment by the author: Theorem 2.2 in this paper is a special case of Theorems 1.1 and 4.1 in the article "Weighted thermodynamic formalism on subshifts and applications", Asian J. Math. 16 (2012), by J. Barral and D. J. Feng. In…
In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the Gauss-Bonnet term (with coefficient $\alpha'$) as a toy example. We find the solution to the $\alpha'$…
We show that spin-density separation in a Bose gas is not restricted to 1D but also occurs in higher dimension. The ratio ($\alpha$) of the intra-species atom-atom interaction strength to the inter-species interaction strength, strongly…
In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower…
In three dimensions, there exist modifications of Einstein's gravity akin to the topologically massive gravity that describe massive gravitons about maximally symmetric backgrounds. These theories are built on the three-dimensional version…
Let $T_\beta$ be the $\beta$-transformation on $[0,1)$ defined by $$T_\beta(x)=\beta x\text{ mod }1.$$ We study the Diophantine approximation of the orbit of a point $x$ under $T_\beta$. Precisely, for given two positive functions…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
In this paper we consider diagonally affine, planar IFS $\Phi=\left\{S_i(x,y)=(\alpha_ix+t_{i,1},\beta_iy+t_{i,2})\right\}_{i=1}^m$. Combining the techniques of Hochman and Feng, Hu we compute the Hausdorff dimension of the self-affine…
In this paper we show that the asymptotic dimension of an unbounded proper metric space is bounded above by a coarse analog of Ponomarev's cofinal dimension of topological spaces, which we call the coarse cofinal dimension. We also show…