arXiv subjects

M. Caruso

Publications and source records attributed to M. Caruso.

9 recordsLinked to original sources

arXiv2023

Equivalent quantum systems

We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects the Hamiltonian operators associated with each quantum system. This bridge allows us to connect different quantum systems, in such a way that studying one of them allows to understand the other through a gauge transformation. Furthermore, we included the case where the Hamiltonian operator can be time-dependent. An application for this construction will be achieved in the theory of control quantum systems.

physics.gen-ph↗

arXiv2022

Classical circuits can simulate quantum aspects

This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system simulation using classical circuits. By synthesizing interaction networks, we accurately simulate quantum systems of varying complexity, from $2-$state to $n-$state systems. Unlike quantum computers, classical approaches do not require stringent conditions, making them more accessible for practical implementation. Our reinterpretation of Born's rule in the context of electrical circuit simulations offers a perspective on quantum phenomena.

quant-ph↗

arXiv2021

Quantum systems simulatability through classical networks

We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum system. Different quantum systems are connected in such way that studying one of them allows to understand the other. This result can be applied to the field of simulation of quantum systems, in order to mimic more complicated quantum systems from another simulatable quantum system. Given that there is a bridge that allows to simulate a particular quantum system on this kind of Hilbert spaces using classical circuits we will provide a general scenario to extend this bridge to simulate the time evolution, via Schrödinger equation, of any of these quantum system using classical circuits. This classical systems can be implemented and controlled more easily in the laboratory than the quantum systems.

quant-ph↗

arXiv2021

An algorithm to represent inbreeding trees

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees and diversity. Groups with a finite number of individuals could give a variety of genetic relationships. { In previous works \cite{PhysRevE.92.052132, PhysRevE.90.022125, JARNE20191}, we have addressed the issue of building inbreeding trees for biparental reproduction using Markovian models. Here, we extend these studies by presenting an algorithm to generate and represent inbreeding trees with no overlapping generations. We explicitly assume a two-gender reproductory scheme, and we pay particular attention to the links between nodes. We show that even for a simple case with a relatively small number of nodes in the tree, there are a large number of possible ways to rearrange the links between generations. We present an open-source python code to generate the tree graph, the adjacency matrix, and the histogram of the links for each different tree representation. We show how this mapping reflects the difference between tree realizations, and how valuable information may be extracted upon inspection of these matrices. The algorithm includes a feature to average several tree realizations, obtain the connectivity distribution, and calculate the average and mean value. We used this feature to compare trees with a different number of generations and nodes. The code presented here, available in Git-Hub, may be easily modified to be applied to other areas of interest involving connections between individuals, extend the study to add more characteristics of the different nodes, etc.

q-bio.PE↗

arXiv2018

Markovian simulation for ancestors trees

We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each generation and use it to constraint the maximum number of the following generation. This new model allows to consider the reproductive preferences of particular species and combine several trees to simulate the behavior of a population. It is also possible to obtain a description analytically, considering the simulation as a theoretical stochastic process. Such process can be generalized in order to use an algorithm associated with it to simulate other similar processes of stochastic nature. The simulation is based in the theoretical model previously presented before.

q-bio.PE↗

arXiv2016

Equivalent Markov processes under gauge group

We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included the case where the sample space is time dependent in a previous work \textit{Phys. Rev. E} \textbf{90}, 022125 (2014). We found a general solution through a dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to the one in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work we show how Markov process in general could be linked via gauge (local) transformations and we present some illustrative examples for this results.

cond-mat.stat-mech↗

arXiv2016

The quantum CP-violating kaon system reproduced in the electronic laboratory (Homage to Nolberto Martinez)

The equivalence between the $\mathrm{Schr\ddot{o}dinger}$ dynamics of a quantum system with a finite number of basis states and a classical dynamics is realized in terms of electric networks. The isomorphism that connects in a univocal way both dynamical systems was applied to the case of neutral mesons, kaons in particular, and the class of electric networks univocally related to the quantum system was analyzed. Moreover, under $CPT$ invariance, the relevant $ε$ parameter that measures $CP$ violation in the kaon system is reinterpreted in terms of network parameters. All these results were explicitly shown by means of both a numerical simulation of the implied networks and by constructing the corresponding circuits.

physics.gen-ph↗

arXiv2014

Markov chain approach to the distribution of ancestors in species of biparental reproduction

We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is not possible to reconstruct the genealogical history of each species along all its generations by means of a geometric progression. This analysis demonstrates that it is possible to rebuild the tree of progenitors by modeling the problem with a Markov chain. For each generation, the maximum number of possible ancestors is different. This brings huge problems for the resolution. We found a solution through a dilation of the sample space, although the distribution defined there takes smaller values respect to the initial problem. In order to correct the distribution for each generation, we introduced the invariance under gauge (local) group of dilations. These ideas can used to study the interaction of several processes and provide a new approach on the problem of the common ancestor. In the same direction, this model also provide some elements that can be used to improve models of animal reproduction.

physics.bio-ph↗

arXiv2011

Equivalence between classical and quantum dynamics. Neutral kaons and electric circuits

An equivalence between the $\mathrm{Schr\ddot{o}dinger}$ dynamics of a quantum system with a finite number of basis states and a classical dynamics is presented. The equivalence is an isomorphism that connects in univocal way both dynamical systems. We treat the particular case of neutral kaons and found a class of electric networks uniquely related to the kaon system finding the complete map between the matrix elements of the effective Hamiltonian of kaons and those elements of the classical dynamics of the networks. As a consequence, the relevant $ε$ parameter that measures CP violation in the kaon system is completely determined in terms of network parameters.

quant-ph↗