Related papers: Geometry of small causal diamonds
The regularity of systolically extremal surfaces is a notoriously difficult problem already discussed by M. Gromov in 1983, who proposed an argument toward the existence of $L^2$-extremizers exploiting the theory of $r$-regularity developed…
Results of Small-Angle Scattering study of diamonds with various types of point and extended defects and different degrees of annealing are presented. It is shown that thermal annealing and/or mechanical deformation cause formation of…
We study the large-scale geometry of t-surfaces -- pairs of perfect t-embeddings and their associated origami maps -- arising from dimer models on Aztec diamonds with periodic edge weights. We prove that these t-surfaces converge to…
We define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to the Hausdorff dimension for metric spaces - that…
It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian…
Isolated, micro-meter sized diamonds are grown by micro-wave plasma chemical vapour deposition technique on Si(001) substrates. Each diamond is uniquely identified by markers milled in the Si substrate by Ga+ focused ion beam. The…
More than a half of asteroids in the main belt have irregular shapes with the ratios of the minor to major axis lengths less than 0.6. One of the mechanisms to create such shapes is collisions between asteroids. The relationship between…
We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals…
We revisit the proposal that coupling two six-dimensional holomorphic Chern-Simons theories generates gaugings throughout the twistor-space diamond relating 6d hCS, 4d self-dual Yang-Mills, 4d Chern-Simons, and 2d integrable models. In…
The $s-$wave meson-baryon scattering is analyzed for the isospin-strangeness $I=1/2, S=0$ and $I=0,S=-1$ sectors, in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. For both sectors, four channels have been…
Recent work has shown that certain integrable and conformal field theories in two dimensions can be given a higher-dimensional origin from holomorphic Chern-Simons in six dimensions. Along with anti-self-dual Yang-Mills and four-dimensional…
We compute the asymptotic expansion of the volume of small sub-Riemannian balls in a contact 3-dimensional manifold, and we express the first meaningful geometric coefficients in terms of geometric invariants of the sub-Riemannian structure
We introduce a new family of closed differential forms naturally associated with minimal graphical submanifolds in Euclidean space, defined in arbitrary codimension. For each minimal graph, we construct an explicit closed form whose…
For causal graphs we propose a definition of proper time which for small scales is based on the concept of volume, while for large scales the usual definition of length is applied. The scale where the change from "volume" to "length" occurs…
In this paper we explore ideas of holography and strings living in the $d+1$ dimensional Anti-de Sitter space $AdS_{d+1}$ in a unified framework borrowed from twistor theory. In our treatise of correspondences between geometric structures…
The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of $\hbar$, it is not straight forwardly possible to find global…
We analyze the ergodic properties of a metallic wavefunction for the Anderson model in a disordered random-regular graph with branching number $k=2.$ A few q-moments $I_q$ associated with the zero energy eigenvector are numerically computed…
In this paper, we generalize the finite generation result of Sormani to non-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces) with full support measures. This is a special case of the Milnor's Conjecture for…
The quasiparticle bands of diamond, a prototype covalent insulator, are herein studied by means of wave-function electronic-structure theory, with emphasis on the nature of the correlation hole around a bare particle. Short-range…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…