arXiv subjects

J. Mateo

Publications and source records attributed to J. Mateo.

3 recordsLinked to original sources

arXiv2019

Bayesian modeling of two-species bacterial competition growth and decline rates in milk

Shiga toxin-producing Escherichia coli O157: H7 is a food-borne pathogen and the major cause of hemorrhagic colitis. Pseudomonas is the genus most frequent psychrotrophic spoilage microorganisms present in milk. Two-species bacterial systems with Escherichia coli O157: H7, non-pathogenic Escherichia coli, and Pseudomonas fluorescens in skimmed milk at 7, 13, 19, or 25 C was studied. Bacterial interactions were modelled after applying a Bayesian approach. No direct correlation between Pseudomonas fluorescent's growth rate and its effect on the maximum population densities of Escherichia coli species was found. The results show the complexity of the interactions between two species into a food model. The use of natural microbiota members to control foodborne pathogens could be useful to improve food safety during the processing and storage of refrigerated foods.

q-bio.PE↗

arXiv2006

On the Path-Integral Derivation of the Anomaly for the Hermitian Equivalent of the Complex $PT$-Symmetric Quartic Hamiltonian

It can be shown using operator techniques that the non-Hermitian $PT$-symmetric quantum mechanical Hamiltonian with a "wrong-sign" quartic potential $-gx^4$ is equivalent to a Hermitian Hamiltonian with a positive quartic potential together with a linear term. A naive derivation of the same result in the path-integral approach misses this linear term. In a recent paper by Bender et al. it was pointed out that this term was in the nature of a parity anomaly and a more careful, discretized treatment of the path integral appeared to reproduce it successfully. However, on re-examination of this derivation we find that a yet more careful treatment is necessary, keeping terms that were ignored in that paper. An alternative, much simpler derivation is given using the additional potential that has been shown to appear whenever a change of variables to curvilinear coordinates is made in a functional integral.

hep-th↗

arXiv2006

An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential

The potential -x^4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has been shown numerically to have a real spectrum, and a proof of reality, involving the correspondence between ordinary differential equations and integral systems, was subsequently constructed for the general class of potentials -(ix)^N. For PT-symmetric but non-Hermitian Hamiltonians the natural PT metric is not positive definite, but a dynamically-defined positive-definite metric can be defined, depending on an operator Q. Further, with the help of this operator an equivalent Hermitian Hamiltonian h can be constructed. This programme has been carried out exactly for a few soluble models, and the first few terms of a perturbative expansion have been found for the potential m^2x^2+igx^3. However, until now, the -x^4 potential has proved intractable. In the present paper we give explicit, closed-form expressions for Q and h, which are made possible by a particular parametrization of the contour in the complex plane on which the problem is defined. This constitutes an explicit proof of the reality of the spectrum. The resulting equivalent Hamiltonian has a potential with a positive quartic term together with a linear term.

quant-ph↗