Related papers: Quantum Cellular Automaton Model for the Generaliz…
We investigate one-dimensional Probabilistic Cellular Automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixture of two different Elementary Cellular Automata rules. All the cells are updated synchronously and…
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this…
For a class of one-dimensional cellular automata, we review and complete the characterization of the invariant measures (in particular, all invariant phase separation measures), the rate of convergence to equilibrium, and the derivation of…
The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
We consider quantum cellular automata on a body-centred cubic lattice and provide a simple derivation of the only two homogenous, local, isotropic, and unitary two-dimensional automata [G. M. D'Ariano and P. Perinotti, Physical Review A 90,…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
We analytically diagonalize a discrete-time on-site interacting fermionic cellular automaton in the two-particle sector. Important features of the solutions sensibly differ from those of analogous Hamiltonian models. In particular, we found…
We present a quantum theory of light based on quantum cellular automata (QCA). This approach allows us to have a thorough quantum theory of free electrodynamics encompassing an hypothetical discrete Planck scale. The theory is particularly…
We describe in detail the solution of the extension of the chiral Gaussian Unitary Ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we…
The role of the $U(1)_A$ anomaly in QCD phenomenology is reviewed, focusing on the relation between quark dynamics and gluon topology. Topics covered include a generalisation of the Witten-Veneziano formula for the mass of the $\eta'$, the…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…
Using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a…
Describing complex phenomena by means of cellular automata (CA) has shown to be a very effective approach in pure and applied sciences. In fact, the number of published papers concerning this topic has tremendously increased over the last…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
We present evidence that operation of QCA (Quantum Cellular Automaton) cells with four dots is possible with an occupancy of 4N+2 electrons per cell (N being an integer). We show that interaction between cells can be described in terms of a…
We compare the eigenvalue spectra of the Dirac operator from a simulation with two mass degenerate dynamical chirally improved fermions with Random Matrix Theory. Comparisons with distribution of k-th eigenvalues (k=1,2) in fixed…