Biomedical subjects

F Borondo

Publications and source records attributed to F Borondo.

At least 19 recordsLinked to original sources

PubMed2006

Scarring by homoclinic and heteroclinic orbits.

In addition to the well-known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated closed circuits in phase space are properly quantized, thus introducing strong quantum correlations. The corresponding quantization rules are also established. This opens the door for developing computationally tractable methods to calculate eigenstates of chaotic systems.

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PubMed2005

Irreversibility with quantum trajectories.

Irreversibility is an important issue for many quantum processes. Loschmidt echoes, originally introduced as a way to gauge sensitivity to perturbations in quantum mechanics, have turned out to be a useful tool for its investigation. Following the philosophy supporting this idea, and using quantum trajectories as defined in the causal interpretation of quantum mechanics due to Bohm, we introduce in this paper a more informative alternative measure for irreversibility. The method is applied to the Bunimovich stadium billiard, a paradigmatic example of chaotic system, that constitutes an excellent model for mesoscopic devices.

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PubMed2005

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.

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PubMed2005

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.

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PubMed2005

Homoclinic motions in the vibrational spectra of floppy systems: the LiCN molecule.

Recent experimental and theoretical methods allowed the efficient investigation of highly excited rovibrational states of molecular systems. At these levels of excitation the correspondence principle holds, and then classical mechanics can provide intuitive views of the involved processes. In this respect, we have recently shown that for completely hyperbolic systems, homoclinic motions, which are known to organize the classical chaotic region in Hamiltonian systems, imprint a clear signature in the corresponding highly excited quantum spectra. In this Communication we show that this result also holds in mixed systems, by considering an application to the floppy LiNCLiCN molecular system.

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PubMed2005

Signatures of homoclinic motion in quantum chaos.

Homoclinic motion plays a key role in the organization of classical chaos in Hamiltonian systems. In this Letter, we show that it also imprints a clear signature in the corresponding quantum spectra. By numerically studying the fluctuations of the widths of wave functions localized along periodic orbits we reveal the existence of an oscillatory behavior that is explained solely in terms of the primary homoclinic motion. Furthermore, our results indicate that it survives the semiclassical limit.

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PubMed2004

Classical invariants and the quantization of chaotic systems.

Due to their exponential proliferation, long periodic orbits constitute a serious drawback in Gutzwiller's theory of chaotic systems. Therefore, it would be desirable that other classical invariants, not suffering from the same problem, could be used in alternative semiclassical quantization schemes. In this Rapid Communication, we demonstrate how a suitable dynamical analysis of chaotic quantum spectra unveils the role played, in this respect, by classical invariant areas related to the stable and unstable manifolds of short periodic orbits.

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PubMed2004

Quantum trajectories in atom-surface scattering with single adsorbates: the role of quantum vortices.

In this work, a full quantum study of the scattering of He atoms off single CO molecules, adsorbed onto the Pt(111) surface, is presented within the formalism of quantum trajectories provided by Bohmian mechanics. By means of this theory, it is shown that the underlying dynamics is strongly dominated by the existence of a transient vortitial trapping with measurable effects on the whole diffraction pattern. This kind of trapping emphasizes the key role played by quantum vortices in this scattering. Moreover, an analysis of the surface rainbow effect caused by the local corrugation that the CO molecule induces on the surface, and its manifestation in the corresponding intensity pattern, is also presented and discussed.

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PubMed2004

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.

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PubMed2003

Different time scales in wave function intensity statistics.

Unstable periodic orbits scar wave functions in chaotic systems. The local short term dynamics also influences the associated spectra that follow the otherwise universal Porter-Thomas intensity distribution. We show here how this deviation extends to other longer periodic orbits sharing some common dynamical characteristics. This indicates that the quantum mechanics of the system can be described quite simply with few orbits, up to the resolution associated with the corresponding lengths.

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PubMed2001

Multifractal analysis of tori destruction in a molecular Hamiltonian system.

In this paper, an analysis of the phase space structure of the isomerizing molecular system LiNC/LiCN, using Poincaré surfaces of section and frequency analysis, is presented. The scaling structure of the frequency map in the chaotic region next to the regular part corresponding to the stable linear isomer LiNC is studied using multifractal analysis. This approach is a way to characterize quantitatively the complexity in the mechanism of the tori destruction in a molecular Hamiltonian system that exhibits soft chaos as the vibrational energy of the system increases.

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PubMed2001

Localization properties of groups of eigenstates in chaotic systems.

In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. 76, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear highly localized not only along periodic orbits but also on the associated manifolds. Moreover, they show in phase space the hyperbolic structure in the vicinity of the orbit, something that translates in configuration space into the structure induced by the corresponding self-focal points. On the other hand, the- quantum dynamics of these functions are also studied. Our results indicate that the probability density first evolves along the unstable manifold emanating from the periodic orbit, and localizes temporarily afterwards on only a few, short related periodic orbits. We believe that this type of study can provide some keys to disentangle the complexity associated with the quantum mechanics of these kind of systems, which permits the construction of a simple explanation in terms of the dynamics of a few classical structures.

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PubMed2000

Beyond the first recurrence in scar phenomena

The scarring effect of short unstable periodic orbits up to times of the order of the first recurrence is well understood. Much less is known, however, about what happens past this short-time limit. By considering the evolution of a dynamically averaged wave packet, we show that the dynamics for longer times is controlled by only a few related short periodic orbits and their interplay.

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PubMed1996