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7 pages, 241 KB

Open AccessArticle

Emergent Space-Time in a Bubble Universe

by James Moffat

Symmetry 2021, 13(4), 729; https://doi.org/10.3390/sym13040729 - 20 Apr 2021

Viewed by 3019

I exploit the close connection between the tessellation of space-time in the Regge calculus and an Eilenberg homology to investigate the deep quantum nature of space-time in a simple bubble universe of a size consistent with the Planck regime. Following the mathematics allows me to define this granulated space-time as the embedding space of the skeleton of a computational spin network inside a quantum computer. This approach can be regarded as a quantum simulation of the equivalent physics. I can, therefore, define a fundamental characterisation of any high-energy physical process at the Planck scale as equivalent to a quantum simulation inside a quantum computer. Full article

(This article belongs to the Special Issue Quantum Gravity)

16 pages, 341 KB

Open AccessArticle

On the Discrete Version of the Schwarzschild Problem

by Vladimir Khatsymovsky

Universe 2020, 6(10), 185; https://doi.org/10.3390/universe6100185 - 17 Oct 2020

Cited by 5 | Viewed by 2713

Abstract

We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge lengths. This elementary length scale is defined by the Planck scale and some free parameter of such a quantum extension of the theory. Besides, Regge action was reduced to an expansion over metric variations between the tetrahedra and, in the main approximation, is a finite-difference form of the Hilbert–Einstein action. Using for the Schwarzschild problem a priori general non-spherically symmetrical ansatz, we get finite-difference equations for its discrete version. This defines a solution which at large distances is close to the continuum Schwarzschild geometry, and the metric and effective curvature at the center are cut off at the elementary length scale. Slow rotation can also be taken into account (Lense–Thirring-like metric). Thus, we get a general approach to the classical background in the quantum framework in zero order: it is an optimal starting point for the perturbative expansion of the theory, finite-difference equations are classical, and the elementary length scale has quantum origin. Singularities, if any, are resolved. Full article

(This article belongs to the Special Issue Selected Papers from the 17th Russian Gravitational Conference —International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17))

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25 pages, 6691 KB

Open AccessReview

Dynamics and Geometry of Icosahedral Order in Liquid and Glassy Phases of Metallic Glasses

by Masato Shimono and Hidehiro Onodera

Metals 2015, 5(3), 1163-1187; https://doi.org/10.3390/met5031163 - 2 Jul 2015

Cited by 16 | Viewed by 7400

Abstract

The geometrical properties of the icosahedral ordered structure formed in liquid and glassy phases of metallic glasses are investigated by using molecular dynamics simulations. We investigate the Zr-Cu alloy system as well as a simple model for binary alloys, in which we can change the atomic size ratio between alloying components. In both cases, we found the same nature of icosahedral order in liquid and glassy phases. The icosahedral clusters are observed in liquid phases as well as in glassy phases. As the temperature approaches to the glass transition point T_g, the density of the clusters rapidly grows and the icosahedral clusters begin to connect to each other and form a medium-range network structure. By investigating the geometry of connection between clusters in the icosahedral network, we found that the dominant connecting pattern is the one sharing seven atoms which forms a pentagonal bicap with five-fold symmetry. From a geometrical point of view, we can understand the mechanism of the formation and growth of the icosahedral order by using the Regge calculus, which is originally employed to formulate a theory of gravity. The Regge calculus tells us that the distortion energy of the pentagonal bicap could be decreased by introducing an atomic size difference between alloying elements and that the icosahedral network would be stabilized by a considerably large atomic size difference. Full article

(This article belongs to the Special Issue Metallic Glasses)

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