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R. Lemus

Publications and source records attributed to R. Lemus.

14 recordsLinked to original sources
arXiv2016

Fidelity, entropy, and Poincaré sections as tools to study the polyad breaking phenomena

The correlation diagram of the vibrational energy spectra associated with the stretching modes of triatomic molecules such as CO$_2$ and H$_2$O is analyzed by means of two interacting Morse oscillators. By considering a linear dependence of the structure and force constants ($x_g=g^o_{rr'}/g^o_{rr}, x_f=f_{rr'}/f_{rr}$) going from the water parameters to the carbon dioxide, it is shown that the fidelity, entropy and Poincaré sections detect the polyad breaking process manifested in the transition from local to normal mode behaviors. Additionally Poincaré sections show a transition to chaos where the polyad cannot be defined.

quant-ph↗
arXiv2015

The role of master regulators in gene regulatory networks

Gene regulatory networks present a wide variety of dynamical responses to intrinsic and extrinsic perturbations. Arguably, one of the most important of such coordinated responses is the one of amplification cascades, in which activation of a few key-responsive transcription factors (termed master regulators, MRs) lead to a large series of transcriptional activation events. This is so since master regulators are transcription factors controlling the expression of other transcription factor molecules and so on. MRs hold a central position related to transcriptional dynamics and control of gene regulatory networks and are often involved in complex feedback and feedforward loops inducing non-trivial dynamics. Recent studies have pointed out to the myocyte enhancing factor 2C (MEF2C, also known as MADS box transcription enhancer factor 2, polypeptide C) as being one of such master regulators involved in the pathogenesis of primary breast cancer. In this work, we perform an integrative genomic analysis of the transcriptional regulation activity of MEF2C and its target genes to evaluate to what extent are these molecules inducing collective responses leading to gene expression deregulation and carcinogenesis. We also analyzed a number of induced dynamic responses, in particular those associated with transcriptional bursts, and nonlinear cascading to evaluate the influence they may have in malignant phenotypes and cancer.

q-bio.MN↗
arXiv2001

A new dynamical group approach to the modified Poschl-Teller potential

The properties of the modified Pöschl-Teller (MPT) potential are outlined. The ladder operators are constructed directly from the wave functions without introducing any auxiliary variable. It is shown that these operators are associated to the $su(2)$ algebra. Analytical expressions for the functions $\sinh(αx)$ and $\frac{\cosh(αx)}α \frac{d}{dx}$ are evaluated from these ladder operators. The expansions of the coordinate $x$ and momentum $\hat p$ in terms of the $su(2)$ generators are presented. This analysis allows to establish an exact quantum-mechanical connection between the $su(2)$ vibron model and the traditional descriptions of molecular vibron.

quant-ph↗
arXiv1998

A local anharmonic treatment of vibrations of methane

The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm$^{-1}$ (and a r.m.s. deviation of 1.16 cm$^{-1}$).

chem-ph↗
arXiv1997

A symmetry adapted approach to vibrational excitations in atomic clusters

An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na$^+_n$ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be$_4$, H$_3^+$, Be$_3$ and Na$_3^+$ clusters.

physics.chem-ph↗
arXiv1997

A comparison between algebraic models of molecular spectroscopy

We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in previous versions of the vibron model, in which the Hamiltonian is expressed in terms of Casimir operators and their products. The inclusion of these new interactions leads to reliable spectroscopic predictions. As an example we study the vibrational excitations of the methane molecule, and compare our results with those obtained in other algebraic models.

physics.chem-ph↗
arXiv1997

Symmetry-adapted algebraic description of stretching and bending vibrations of ozone

The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U(2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O_3 and 18 O_3 yields a r.m.s. deviation of 2.5 and 1.0 1/cm, respectively.

chem-ph↗
arXiv1997

Comment on ``Boson-realization model for the vibrational spectra of tetrahedral molecules''

An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry adapted algebraic approach based on U(2) algebras.

physics.chem-ph↗
arXiv1996

A symmetry-adapted algebraic approach to molecular spectroscopy

We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have identified interaction terms that were absent in previous formulations of the vibron model. The inclusion of these new interactions leads to reliable spectroscopic predictions. We illustrate the method for the D_3h triatomic molecules, H_3^+, Be_3 and Na_3, and the T_d molecules, Be_4 and CH_4.

physics.chem-ph↗
arXiv1996

Application of a symmetry-adapted algebraic model to the vibratioinal spectrum of methane

The stretching and bending vibrations of methane are studied in the framework of a symmetry-adapted algebraic model. The model is based on the realization of the one-dimensional Morse potential in terms of a $U(2)$ algebra. For the 44 observed energies we obtain a fit with a r.m.s. deviation of 1.16 cm$^{-1}$ which is an order of magnitude more accurate than previous algebraic calculations.

physics.chem-ph↗
arXiv1996

A general algebraic model for molecular vibrational spectroscopy

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.

chem-ph↗
arXiv1996

A Symmetry Adapted Approach to Molecular Spectroscopy: The Anharmonic Oscillator Symmetry Model

We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and configuration space formulations, by means of which new interactions are found in the algebraic model, leading to reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules and the ${\cal T}_d$ Be-cluster.

chem-ph↗