arXiv subjects

Diógenes Galetti

Publications and source records attributed to Diógenes Galetti.

6 recordsLinked to original sources

arXiv2019

The delimiting/frontier lines of the constituents of matter

Looking at the \emph{chart of nuclides} displayed at the URL of the International Atomic Energy Agency (IAEA) \cite{IAEA} -- that contains all the known nuclides, the natural and those produced artificially in labs -- one verifies the existence of two, not quite regular, \emph{delimiting lines} between which dwell all the nuclides constituting matter. These lines are established by the highly unstable radionuclides located the most far away from those in the central locus, the\emph{valley of stability}. Here, making use of the "old" semi-empirical mass formula for stable nuclides together with the energy-time uncertainty relation of quantum mechanics, by a simple calculation we show that the obtained \emph{frontier lines}, for proton and neutron excesses, present an appreciable agreement with the delimiting lines. For the sake of presenting a somewhat comprehensive panorama of the matter in our Universe and their relation with the frontier lines, we narrate, in brief, what is currently known about the astrophysical nucleogenesis processes.

nucl-th↗

arXiv2018

An algorithm for hiding and recovering data using matrices

We present an algorithm for the recovery of a matrix $\mathbb{M}$ % (non-singular $\in $ $\mathbb{C}^{N\times N}$) by only being aware of two of its powers, $\mathbb{M}_{k_{1}}:=\mathbb{M}^{k_{1}}$ and $\mathbb{M}% _{k_{2}}:=\mathbb{M}^{k_{2}}$ ($k_{1}>k_{2}$) whose exponents are positive coprime numbers. The knowledge of the exponents is the key to retrieve matrix $\mathbb{M}$ out from the two matrices $\mathbb{M}_{k_{i}}$. The procedure combines products and inversions of matrices, and a few computational steps are needed to get $\mathbb{M}$, almost independently of the exponents magnitudes. Guessing the matrix $\mathbb{M}$ from the two matrices $\mathbb{M}_{k_{i}}$, without the knowledge of $k_{1}$ and $k_{2}$, is comparatively highly consuming in terms of number of operations. If a private message, contained in $\mathbb{M}$, has to be conveyed, the exponents can be encrypted and then distributed through a public key method as, for instance, the DF (Diffie-Hellman), the RSA (Rivest-Shamir-Adleman), or any other.

cs.CR↗

arXiv2017

Modeling a vehicular traffic network. Part I

We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a sequence of $n$ consecutive steps, or units of time. An essential approach consists in using, as an "a priori" information, previous observations and measurements. The formal tools used in our analysis consists in: (1) associating a digraph to the network where the edges correspond to arteries and the vertices with loops represent the sites. (2) From an initial set of numbers, that are the distribution of vehicles within the network, we construct a matrix that we transform into a stochastic matrix (SM) by normalizing the rows, whose entries are now transition probabilities. This matrix becomes the generator of the evolution of the traffic flow. And (3), we use the Perron-Frobenius theory for a formal analysis. We investigate three models: (a) a closed four-site network having a conserved number of vehicles; (b) to this network we add an influx and an outflux of vehicles to characterize an open system; asymptotically, $n \rightarrow \infty$, the SM raised to the power $n$ goes to a unique stationary matrix. And (c), we construct a nonlinear model because the formal structure permits the existence of several ($L$) stationary states for the distribution of vehicles at each site, that alternate cyclically with time. Each state represents the traffic for $L$ different moments. These models were used to analyze the traffic in a sector of the city of Tigre, located in the province of Buenos Aires, Argentina. The results are presented in a following paper.

physics.soc-ph↗

arXiv2015

Maximally genuine multipartite entangled mixed X-states of N-qubits

For every possible spectrum of $2^N$-dimensional density operators, we construct an $N$-qubit X-state of same spectrum and maximal genuine multipartite (GM-) concurrence, hence characterizing a global unitary transformation that --- constrained to output X-states --- maximizes the GM-concurrence of an arbitrary input mixed state of $N$ qubits. We also apply semidefinite programming methods to obtain $N$-qubit X-states with maximal GM-concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the role, the so-called X-MEMS. Furthermore, we introduce a numerical strategy to tailor a quantum operation that converts between any two given density matrices using a relatively small number of Kraus operators. We apply our strategy to design short operator-sum representations for the transformation between any given $N$-qubit mixed state and a corresponding X-MEMS of same purity.

quant-ph↗

arXiv2014

Entanglement universality of two-qubit X-states

We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states.

quant-ph↗

arXiv2013

Spin squeezing and entanglement via finite-dimensional discrete phase-space description

We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson-Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations -> entanglement -> squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems.

quant-ph↗