Using Lagrangian descriptors to calculate the Maslov index of periodic orbits.

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of nonintegrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.

Order-chaos transition in correlation diagrams and quantization of period orbits.

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)0031-900710.1103/PhysRevLett.80.944] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing the Planck constant, we induced a transition from order to chaos, in which scarred wave functions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well-defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.

Impact of Zulla cover crop in vineyard on the musts volatile profile of Vitis vinifera L. cv Syrah.

Grape aromatic characteristics are very important for producing quality wines. There have been very few studies on concentrations of volatile compounds in grape berries from vines with cover crops. For this reason, the aim of this work was to evaluate the influence of "Zulla" cover crop on the volatile profiles of organically grown Syrah variety grapes. For this purpose, volatile profiles of grapes obtained from vines with three different amounts of cover crop (one line, two lines, and four lines) and without cover crop, over three harvests (2019, 2020, and 2021) were determined. Moreover, a comparative study of conventional and organic crops, both submitted to soil tillage, was performed. The grape samples came from a warm climate zone. Must volatile compounds were determined by sequential sorptive extraction with Twisters by immersion (SBSE) and headspace (HSSE), followed by GC-MS analysis. A total of 160 compounds were determined and most of them were influenced by the presence of cover crop. However, the results showed an important influence of the harvest year over agronomic practices. Therefore, organic cultivation using Zulla cover crop seems to be a suitable tool for the implementation of friendly ecosystem management in a warm climate Syrah vineyard.

Correspondence between classical and quantum resonances.

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li⇆Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series to ℏ=0 unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit ℏ→0. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.

Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case.

The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum manifestations of chaos in such dynamical systems. In this paper, we consider the highly nonlinear K-CN molecule, showing how the regular classical structures, i.e., Kolmogorov-Arnold-Moser tori, existing in the mixed classical phase space appear in the quantum levels correlation diagram as emerging diabatic states, something that remains hidden when only the actual value of the Planck constant is considered. Additionally, a quantum transition from order to chaos is unveiled with the aid of these correlation diagrams, where it appears as a frontier of scarred functions.

Shannon entropy at avoided crossings in the quantum transition from order to chaos.

Shannon entropy is studied for the series of avoided crossings that characterize the transition from order to chaos in quantum mechanics. In order to be able to study jointly this entropy for discrete and continuous probability, calculations have been performed on a quantized map, the kicked Harper map, resulting in a different behavior, as order-chaos transition takes place, for the discrete (position representation) and continuous (coherent state representation) cases. This different behavior is analyzed in terms of the distribution of zeros of the Husimi function.

Above Saddle-Point Regions of Order in a Sea of Chaos in the Vibrational Dynamics of KCN.

The dynamical characteristics of a region of regular vibrational motion in the sea of chaos above the saddle point corresponding to the linear C-N-K configuration is examined in detail. To explain the origin of this regularity, the associated phase space structures were characterized using suitably defined Poincaré surfaces of section, identifying the different resonances between the stretching and bending modes, as a function of excitation energy. The corresponding topology is elucidated by means of periodic orbit analysis.

A mesoscopic stochastic model for the specific consumption rate in substrate-limited microbial growth.

The specific consumption rate of substrate, as well as the associated specific growth rate, is an essential parameter in the mathematical description of substrate-limited microbial growth. In this paper we develop a completely new kinetic model of substrate transport, based on recent knowledge on the structural biology of transport proteins, which correctly describes very accurate experimental results at near-zero substrate concentration values found in the literature, where the widespread Michaelis-Menten model fails. Additionally, our model converges asymptotically to Michaelis-Menten predictions as substrate concentration increases. Instead of the single active site enzymatic reaction of Michaelis-Menten type, the proposed model assumes a multi-site kinetics, simplified as an apparent all-or-none mechanism for the transport, which is controlled by means of the local substrate concentration in the close vicinity of the transport protein. Besides, the model also assumes that this local concentration is not equal to the mean substrate concentration experimentally determined in the culture medium. Instead, we propose that it fluctuates with a mostly exponential distribution of Weibull type.

Quantum control of isomerization by robust navigation in the energy spectrum.

In this paper, we present a detailed study on the application of the quantum control technique of navigation in the energy spectrum to chemical isomerization processes, namely, CN-Li⇆ Li-CN. This technique is based on the controlled time variation of a Hamiltonian parameter, an external uniform electric field in our case. The main result of our work establishes that the navigation involved in the method is robust, in the sense that quite sizable deviations from a pre-established control parameter time profile can be introduced and still get good final results. This is specially relevant thinking of a experimental implementation of the method.

Distribution of zeros of the Husimi function in systems with degeneracy.

The distribution of zeros of the Husimi function of energy eigenstates has proven to be a very useful tool for the characterization of the quantum transition from order to chaos in systems without degeneracy. In this paper, we show, by means of calculations on the Hénon-Heiles Hamiltonian system, that the quantum order-chaos transition in systems with degeneracy can also be characterized through the distribution of the Husimi function zeros, providing that the appropriate linear combination of degenerate eigenstates is used. If using an arbitrary linear combination, spurious results can be achieved, suggesting a wrong premature quantum transition to chaos.

Breast cancer management in the elderly

The increase in life expectancy in the western world means that we are faced with patients diagnosed with breast cancer in old age with increasing frequency. The management of these cases is a challenge for the oncologist, who must take into account the conditions associated with advanced age and the lack of trials in this population. In this review, we addressed the incorporation of geriatric assessment methods that may be useful in making decisions, the particular biological characteristics of breast cancer in elderly patients and their treatment in both localized and advanced disease. Finally, we collected recommendations based on scientific evidence regarding the monitoring and life-style after finishing treatment (AU)

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Breast cancer management in the elderly.

The increase in life expectancy in the western world means that we are faced with patients diagnosed with breast cancer in old age with increasing frequency. The management of these cases is a challenge for the oncologist, who must take into account the conditions associated with advanced age and the lack of trials in this population. In this review, we addressed the incorporation of geriatric assessment methods that may be useful in making decisions, the particular biological characteristics of breast cancer in elderly patients and their treatment in both localized and advanced disease. Finally, we collected recommendations based on scientific evidence regarding the monitoring and life-style after finishing treatment.

Ab initio potential energy surface for the highly nonlinear dynamics of the KCN molecule.

An accurate ab initio quantum chemistry study at level of quadratic configuration interaction method of the electronic ground state of the KCN molecule is presented. A fitting of the results to an analytical series expansion was performed to obtain a global potential energy surface suitable for the study of the associated vibrational dynamics. Additionally, classical Poincaré surfaces of section for different energies and quantum eigenstates were calculated, showing the highly nonlinear behavior of this system.

Onset of quantum chaos in molecular systems and the zeros of the Husimi function.

The distribution of zeros of the Husimi function has proven a useful tool in the characterization of regular and chaotic quantum states of dynamical systems. In a previous paper [Phys. Rev. E 82, 026201 (2010)], we showed how the quantum transition from order to chaos in three different molecular systems (LiCN, HCN, and HO(2)) can be understood by means of the correlation diagram of eigenenergies versus the Planck's constant. An order-chaos frontier of scars (eigenstates localized over unstable and stable complementary, in the sense of the Poincaré-Birkhoff theorem, periodic orbits) was observed. In this paper, we show how the distribution of zeros of the Husimi function can be related to the onset of chaos in these molecular systems, showing a very interesting feature at the frontier of scars; namely, some zeros of the Husimi function localize over the stable and unstable fixed points corresponding to the two complementary periodic orbits, this representing the quantum equivalent to the Poincaré-Birkhoff theorem.

Poincaré-Birkhoff theorem in quantum mechanics.

Quantum manifestations of the dynamics around resonant tori in perturbed hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.

Scars at the edge of the transition from order to chaos in the isomerizing molecular systems LiNC-LiCN and HCN-HNC, and HO2.

Correlation diagrams of energy levels using ℏ as the varying parameter have proven very useful in the characterization of quantum vibrational dynamics of small polyatomic molecules, specially in relation to the transition from order to chaos. In this paper, we present calculations of such correlation diagrams for three molecular systems with very different characteristics, which can be traced down to the topology of their potential energy surfaces. By studying the broad avoided crossings existing in the diagrams, we show that the transition from regular to irregular states always corresponds to a frontier formed by scarred states.

The onset of chaos in the vibrational dynamics of LiNC/LiCN.

Recent advances in vibrational spectroscopy have greatly enhanced the possibilities of research of highly excited states in molecular systems of moderate size. At sufficiently high level of excitation the correspondence principle holds, and classical mechanical arguments constitute a useful interpretative tool. The corresponding dynamics often become very complex specially in systems with floppy degrees of freedom, and periodic motion plays an important role for its understanding. In this paper, we present a computational procedure to systematically calculate periodic orbits of LiNCLiCN with a given symmetry, that has the additional advantage of providing a useful insight into the onset of chaos in this system.

Vibrational dynamics of the floppy LiNC/LiCN molecular system.

Modern spectroscopical techniques allow the efficient experimental investigation of highly excited vibrational states in molecular systems. On the theoretical side, powerful computational methods have also been developed for the calculation of the corresponding energy levels and wave functions, and their interpretation. In this paper we use a combination of two such methods, namely, the distribution of zeroes in the Husimi function and energy-level correlation diagrams, to discuss a classification scheme, for the lowest hundred vibrational levels of the LiNC/LiCN floppy molecular system, based on their dynamical characteristics.

Mujer de 26 años con náuseas y distensión abdominal / A 26 years woman with nauseas and abdominal distension

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Topology of the distribution of zeros of the Husimi function in the LiNC/LiCN molecular system.

Phase space representations of quantum mechanics constitute useful tools to study vibrations in molecular systems. Among all possibilities, the Husimi function or coherent state representation is very widely used, its maxima indicating which regions of phase space are relevant in the dynamics of the system. The corresponding zeros are also a good indicator to investigate the characteristics of the eigenstates, and it has been shown how the corresponding distributions can discriminate between regular, irregular, and scarred wave functions. In this paper, we discuss how this result can be understood in terms of the overlap between coherent states and system eigenfunctions.