arXiv subjects

R. V. Ramos

Publications and source records attributed to R. V. Ramos.

At least 19 recordsLinked to original sources

arXiv2025

Quantum secure direct communication of continuous-time signals using Whittaker Nyquist Shannon theorem

In the present work, we provide a new quantum secure direct communication protocol and its experimental implementation. The proposed protocol can be used to transfer, in a secure way, continuous signals, like audio signal, from Alice to Bob. The security is guaranteed by the quantum nature of optical signals and the Whittaker-Nyquist-Shannon theorem. Furthermore, it can be easily implemented with common optical devices that are commercially available.

quant-ph↗

arXiv2023

Solving the Fermat and Fibonacci Equations with the Lambert-Tsallis Wq Function

In this work, the Lambert-Tsallis Wq function is used to provide analytical solutions of fractional polynomials of the type ax^r+bx^s+c = 0. This class of fractional polynomial appears in several areas of physics as well it is in the heart of some famous mathematical problems, like the Fermat and Fibonacci equations. Therefore, analytical solutions for the equations A^x + B^x = C^x and q1^x-q2^x=ysqrt(5), where q1=(1+sqrt(5))/2 and q2=(sqrt(5)-1))/2, are also provided.

math.GM↗

arXiv2020

Transcendental Numbers and the Lambert-Tsallis Function

To decide upon the arithmetic nature of some numbers may be a non-trivial problem. Some cases are well know, for example exp(1) and W(1), where W is the Lambert function, are transcendental numbers. The Tsallis q-exponential, e_q (z), and the Lambert-Tsallis W_q (z) function, where q is a real parameter, are, respectively, generalizations of the exponential and Lambert functions. In the present work we use the Gelfond-Schneider theorem in order to show the arithmetic conditions on q and z such that W_q (z) and exp_q (z) are transcendental.

math.NT↗

arXiv2020

Estimation of the Randomness of Continuous and Discrete Signals Using the Disentropy of the Autocorrelation

The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the lack of randomness in a speech signal may indicate the speaker is a machine. Hence, to quantify the amount of randomness in a signal is an important task in many different areas. In this direction, the present work proposes to use the disentropy of the autocorrelation function as a measure of randomness. Examples using noisy and chaotic signals are shown.

physics.data-an↗

arXiv2020

The q-Diode

The present work introduces the new function Rq,Q(z), solution of the equation Rq,Q(z) XQ expq(Rq,Q(z)) = z. It is shown this new function can be used to construct new disentropy as well it is used to model the q-diode, a hypothetical electronic device whose electrical current depends q-exponentially on the voltage between its terminals.

physics.gen-ph↗

arXiv2020

Applications of Lambert-Tsallis and Lambert-Kaniadakis Functions in Differential and Difference Equations with Deformed Exponential Decay

The analysis of a dynamical system modelled by differential (continuum case) or difference equation (discrete case) with deformed exponential decay, here we consider Tsallis and Kaniadakis exponentials, may require the use of the recently proposed deformed Lambert functions: the Lambert-Tsallis and Lambert-Kaniadakis functions. In this direction, the present work studies the logistic map with deformed exponential decay, using the Lambert-Tsallis and the Lambert-Kaniadakis functions to determine the stable behaviour and the dynamic of the disentropy in the weak chaotic regime. Furthermore, we investigate the motion of projectile when the vertical motion is governed by a non-linear differential equation with Tsallis exponential in the coefficient of the second order derivative. In this case, we calculated the range of the projectile using the Lambert-Tsallis function.

cond-mat.stat-mech↗

arXiv2020

Quantum and Classical Information Theory with Disentropy

Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication to medical image processing, for example. Now, entropy meets its dual, the disentropy. As such, the disentropy can be used everywhere entropy is used, offering a different point of view: since entropy is a measure of disorder or uncertainty, disentropy is a measure of order or certainty. Thus, important concepts of physics can be rewritten using disentropy instead of entropy. Although there is a large range of problems that can be solved using entropy or disentropy, there are situations where only the disentropy can be used. This happens because the disentropy can provide a real output value when its argument is negative, while the entropy cannot. Thus, it is possible to calculate, for example, the disentropy of quasi-probability distributions like the Wigner function of highly quantum states. In this direction, the present work shows applications of the disentropy in a small list of problems: quantum and classical information theory, black hole thermodynamics, image processing and number theory.

quant-ph↗

arXiv2019

Radial basis function network using Lambert-Tsallis Wq function

The present work brings two applications of the Lambert-Tsallis Wq function in radial basis function networks (RBFN). Initially, a RBFN is used to discriminate between entangled and disentangled bipartite of qubit states. The kernel used is based on the Lambert-Tsallis Wq function for q = 2 and the quantum relative disentropy is used as distance measure between quantum states. Following, a RBFN with the same kernel is used to estimate the probability density function of a set of data samples.

quant-ph↗

arXiv2018

The Lambert-Tsallis Wq Function

In the present work, we introduce the Lambert-Tsallis Wq function. It is a generalization of the Lambert W function, that solves the equation Wq(x)expq(Wq(x)) = x, where expq(x) is the q-exponential used by Tsallis in nonextensive statistical mechanics. We show its numerical calculation and some applications.

cond-mat.stat-mech↗

arXiv2018

A Non-Linear Difference Equation for Calculation of the Zeros of the Riemann Zeta-Function on the Critical Line

In this work, we present a non-linear difference equation for calculation of the zeros of the Riemann's zeta-function on the critical line. Our proposed non-linear map uses the Lambert W function and it can be easily implemented in a mathematical software. In order to check the quality of the zeros calculated, we show the factorization of an integer number by the calculation of the discrete cosine Riemann transform.

math.NT↗

arXiv2017

Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis

In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of the type 0/0 in the inner product of two coherent states. In the second case, the Hilber-Polya conjecture with a quantum circuit is considered. In the third case, randomness, entanglement and the Moebius function are used to discuss the RH. At last, in the fourth case, the RH is discussed by inverting the first derivative of the Chebyshev function. The results obtained reinforce the belief that the RH is true.

physics.gen-ph↗

arXiv2017

Quantum-Chaotic Cryptography

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

quant-ph↗

arXiv2016

Synchronization of Two and Three Optoeletronic Oscillators Operating in Chaotic Regime: Numerical Simulations and Schemes for Secure Communication

In this work we show a strategy for synchronization of three optoelectronic oscillators (OEO) operating in chaotic regime. Two applications of synchronized OEOs in secure communications are considered. In the first one the OEO is used to produce a pseudo-random bit sequence. The second application is an optical setup for secure transmission of sampled analog signals. Using numerical simulations, we calculated the bit error rate taking into account parameter mismatch noise and Gaussian noise in the input optical power. The conditions for error rate of up to 15% during key generation are shown.

physics.optics↗

arXiv2015

Quantum search followed by classical search versus quantum search alone

In this work, we show that the usage of a quantum gate that gives extra information about the solution searched permits to improve the performance of the search algorithm by switching from quantum to classical search in the appropriated moment. A comparison to the case where only quantum search is used is also realized.

quant-ph↗

arXiv2015

Double Quantum Well Triple Barrier Structures: Analytical and Numerical Results

In this work we show an analytical result for the scattering in a particular type of double quantum well triple barrier structure and numerical results, via the Numerov method, for bound states of a double quantum well triple barrier inside of a infinite quantum well. For the last, we consider both, constant and position dependent mass.

quant-ph↗

arXiv2015

Numerical Solution of the 1D-Schrödinger Equation with Pseudo-Delta Barrier Using Numerov Method

In this work, aiming to solve numerically the Schrödinger equation with a Dirac delta function potential, we use the Numerov method to solve the time independent 1D-Schrödinger equation with potentials of the form V(x) + deltap(x), where deltap(x) is a pseudo-delta function, a very high and thin barrier. The numerical results show good agreement with analytical results found in the literature. Furthermore, we show the numerical solutions of a system formed by three delta function potentials inside of an infinite quantum well and the harmonic potential with position dependent mass and a delta barrier in the center.

quant-ph↗

arXiv2015

Considerations about the randomness of bit strings originated from sequences of integer numbers according to a simple quantum computer model

This work uses a simple quantum computer model to discuss the randomness of bit strings originated from integer sequences. The considered quantum computer model has three elements: a processing unit responsible for a mathematical operation, an initial equally weighted superposition and a quantum state used as resource. The randomness depends on the last.

quant-ph↗

arXiv2014

Riemann Hypothesis as an Uncertainty Relation

Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator is introduced and used to transform the Riemann's hypothesis in a Heisenberg-type uncertainty relation, offering a new way for studying the zeros of Riemann's function

math-ph↗