arXiv subjects

P. Roman

Publications and source records attributed to P. Roman.

6 recordsLinked to original sources

arXiv2026

Polynomial Transformations of Jacobi Matrices, Matrix valued Orthogonal polynomials and Random Walks

In this paper, we study matrix valued orthogonal polynomials whose block Jacobi matrix is $Θ(J)$, viewed in blocks of size $m=\degΘ$, where $J$ is a tridiagonal Jacobi matrix and $Θ$ is a scalar polynomial. We identify their matrix measure of orthogonality intrinsically as the push-forward, under $Θ$, of a matrix measure constructed from the original scalar orthogonal polynomials. We formulate reducibility in the push-forward variable and prove that the $2\times2$ Hermite family associated with $Θ(x)=x^2+α_1x$ is irreducible for $α_1\neq0$ and reducible for $α_1=0$. This problem is motivated by random walks with transition matrix $Θ(J)$. For these models, we derive scalar and block Karlin--McGregor representations for the powers of $Θ(J)$. We apply the construction to the mixed one- and two-ball Ehrenfest chain, obtaining explicit spectral measures, spectral multiplicities, and transition formulas, and we conclude with the corresponding $k$-ball and multi-ball extensions.

math.PR↗

arXiv2024

Quantum simulation of entanglement dynamics in a quantum processor

We implement a five-qubit protocol in IBM quantum processors to study entanglement dynamics in a two qubit system in the presence of a simulated environment. Specifically, two qubits represent the main system, while another two qubits serve as the environment. Additionally, we employ an auxiliary qubit to estimate the quantum entanglement. Specifically, we observe the sudden death and sudden birth of entanglement for different inital conditions that were simultaneously implemented on the IBM 127-qubit quantum processor \textit{ibm$\_$brisbane}. We obtain the quantum entanglement evolution of the main system qubits and the environment qubits averaging over $N=10$ independent experiments in the same quantum device. Our experimental data shows the entanglement and disentanglement signatures in system and enviroment qubits, where the noisy nature of current quantum processors produce a shift on times signaling sudden death or sudden birth of entanglement. This work takes relevance showing the usefulness of current noisy quantum devices to test fundamental concepts in quantum information.

quant-ph↗

arXiv2014

CO gas inside the protoplanetary disk cavity in HD 142527: disk structure from ALMA

Inner cavities and annular gaps in circumstellar disks are possible signposts of giant planet formation. The young star HD 142527 hosts a massive protoplanetary disk with a large cavity that extends up to 140 au from the central star, as seen in continuum images at infrared and millimeter wavelengths. Estimates of the survival of gas inside disk cavities are needed to discriminate between clearing scenarios. We present a spatially and spectrally resolved carbon monoxide isotopologue observations of the gas-rich disk HD 142527, in the J=2-1 line of 12CO, 13CO and C18O, obtained with the Atacama Large Millimeter Array (ALMA). We detect emission coming from inside the dust-depleted cavity in all three isotopologues. Based on our analysis of the gas in the dust cavity, the 12CO emission is optically thick, while 13CO and C18O emission are both optically thin. The total mass of residual gas inside the cavity is about 1.5-2 Jupiter masses. We model the gas with an axisymmetric disk model. Our best fit model shows that the cavity radius is much smaller in CO than it is in millimeter continuum and scattered light observations, with a gas cavity that does not extend beyond 105 au (at 3-sigma). The gap wall at its outer edge is diffuse and smooth in the gas distribution, while in dust continuum it is manifestly sharper. The inclination angle, as estimated from the high velocity channel maps, is 28+/-0.5 degrees, higher than in previous estimates, assuming a fix central star mass of 2.2 Solar masses.

astro-ph.EP↗

arXiv2007

The generalized matrix valued hypergeometric equation

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in \cite{T2}. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in \cite{T2} to identify the corresponding matrix hypergeometric functions ${}_nF_m$. We prove that, if n=m+1, this functions are analytic for |z|<1 and we give a necesary condition for the convergence on the unit circle |z|=1.

math-ph↗

arXiv2007

A sequence of matrix valued orthogonal polynomials associated to spherical functions

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, with respect to a weight W, that are eigenfunctions of a second order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We also find other second order differential operator E symmetric with respect to W and we describe the algebra generated by D and E.

math.RT↗

arXiv1999

The ISOCAM/LW Detector Dark Current Behaviour

We describe the calibration, measurements and data reduction, of the dark current of the ISOCAM/LW detector. We point-out the existence of two significant drifts of the LW dark-current, one throughout the ISO mission, on a timescale of days, another within each single revolution, on a timescale of hours. We also show the existence of a dependence of the dark current on the temperature of the ISOCAM detector. By characterizing all these effects through polynomial fittings, we build a model for the LW calibration dark, that depends on the epoch of observation (parametrized with the revolution number and the time elapsed in that given revolution since the activation) and on the temperature of the ISOCAM detector. The model parameters are tuned for each of ISOCAM/LW pixel. We show that the modelling is very effective in taking into account the dark-current variations and allows a much cleaner dark subtraction than using a brute average of several calibration dark images. The residuals of the LW model-dark subtraction are, on average, similar to the pre-launch expectation.

astro-ph↗