scholarly journals Dynamical Triangulation Induced by Quantum Walk

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 128 ◽  
Author(s):  
Quentin Aristote ◽  
Nathanaël Eon ◽  
Giuseppe Di Molfetta

We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2 - manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as t α e − β t 2 , where α and β parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations.

2015 ◽  
Vol 2 (3) ◽  
pp. 243-252 ◽  
Author(s):  
Giuseppe Di Molfetta ◽  
Lauchlan Honter ◽  
Ben B. Luo ◽  
Tatsuaki Wada ◽  
Yutaka Shikano

2017 ◽  
Vol 17 (9&10) ◽  
pp. 810-824 ◽  
Author(s):  
Pablo Arrighi ◽  
Stefno Facchini

A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently it was discovered that prior grouping and encoding allows for more general continuum limit equations (e.g. the Dirac equation in (1+ 1) curved spacetime). In this paper, we extend these results to arbitrary space dimension and internal degree of freedom. We recover an entire class of PDEs encompassing the massive Dirac equation in (3 + 1) curved spacetime. This means that the metric field can be represented by a field of local unitaries over a lattice.


2015 ◽  
Vol 2 (3) ◽  
pp. 253-254
Author(s):  
Giuseppe Di Molfetta ◽  
Lauchlan Honter ◽  
Ben B. Luo ◽  
Tatsuaki Wada ◽  
Yutaka Shikano

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Pablo Arrighi ◽  
Giuseppe Di Molfetta ◽  
Iván Márquez-Martín ◽  
Armando Pérez

2019 ◽  
Vol 11 (1) ◽  
pp. 62-81
Author(s):  
Matiur Rahman ◽  
Muhammad Mustafa ◽  
Lonnie Turpin

PurposeThis paper aims to empirically explore the effects of globalization, corruption perception, political stability, macroeconomic vulnerability and gross domestic savings on illicit financial outflows of 60 developing countries from 2004 to 2013.Design/methodology/approachPedroni’s heterogeneous panel data methodology for co-integration is applied. Panel unit root tests reveal non-stationarity of each variable in level, and a battery of seven panel co-integration tests largely confirm long-run equilibrium relationship among the variables under study.FindingsThe panel vector error correction model estimates show that variables tend to converge toward long-run equilibrium at a very slow pace amid some short-term random fluctuations. At the same time, political stability reduces illicit financial outflows.Originality/valueThere are enhancing impacts of globalization, corruption perception, macroeconomic vulnerability and domestic gross savings on illicit financial outflows. Political stability dampens such outflows. To the authors’ knowledge, such studies are either very scant or non-existent.


Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.


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