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F. Borondo

Universidad Autónoma de Madrid, Departamento de Química, Faculty Member

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Loughborough University

Monash University

Alexander Turbiner

Massimiliano Picciani

Peter Saalfrank

Fernando Lombardo

Diana Monteoliva

Universidad Nacional de La Plata

Université de Perpignan-Via Domitia

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Papers by F. Borondo

Finite-barrier corrections for multidimensional barriers in colored noise

Physical Review E, 2019

The usual identification of reactive trajectories for the calculation of reaction rates requires ... more The usual identification of reactive trajectories for the calculation of reaction rates requires very timeconsuming simulations, particularly if the environment presents memory effects. In this paper, we develop a method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.

Periodic Orbits and Quantum Mechanics of Molecular Hamiltonian Systems

Hamiltonian Systems with Three or More Degrees of Freedom, 1999

... York. 4. Borondo, F. and Benito, RM (1995) in E. Yurtsever (ed), Frontiers of Chemical Physic... more

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

Physical Review E, 2020

The correlation diagrams of vibrational energy levels considering the Planck constant as a variab... more 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.

Correspondence principle, semiclassical quantization and chaos in the dynamics of triatomic molecules

Irregular many-body dynamics of spinor Bose-Einstein condensates in an optical lattice

Physical Review E, 2008

The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in a... more The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in an optical lattice, where light-induced and static magnetic dipole-dipole interactions originate the interplay of the condensate at each site, are investigated. Classical-quantum correspondence in the large-spin limit is studied. Quantum chaotic features are studied through analysis of the irregular spectrum and time evolution of the Shannon entropy of wave packets. We show how the optical lattice strength influences the system dynamics, and is responsible for a transition from regular to irregular bahavior.

Vortex dynamics and their interactions in quantum trajectories

Journal of Physics A: Mathematical and Theoretical, 2007

Theoretical study of the rotational predissociation of the c 3πu state of H2

Chemical Physics Letters, 1988

Abstract We present a theoretical study of the predissociation of the c 3Πu state of H2. The rota... more Abstract We present a theoretical study of the predissociation of the c 3Πu state of H2. The rotational coupling responsible for this process is accurately calculated for the internuclear distances of interest, and the validity of the pure precession approximation in this particular case is analyzed. Our numerical results for the predissociative lifetimes of the vibrational levels of this state are compared with previous experimental and theoretical values.

Deep learning methods for the computation of vibrational wavefunctions

Communications in Nonlinear Science and Numerical Simulation, 2021

• Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining ... more • Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining good approximations to the corresponding eigenenergies and eigenfunctions. • Modifications of the neural network to make it suitable for obtaining highly excited eigenfunctions, where no obvious nodal patterns exist, and quantum numbers are not well defined. • Application to typical molecular potentials.

Deep learning methods for the computation of vibrational wavefunctions

Communications in Nonlinear Science and Numerical Simulation, 2021

• Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining ... more • Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining good approximations to the corresponding eigenenergies and eigenfunctions. • Modifications of the neural network to make it suitable for obtaining highly excited eigenfunctions, where no obvious nodal patterns exist, and quantum numbers are not well defined. • Application to typical molecular potentials.

Rate calculation with correlated noise

arXiv: Chaotic Dynamics, 2016

The usual identification of reactive trajectories for the calculation of reaction rates requires ... more The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a new method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.

Lagrangian descriptors and regular motion

Communications in Nonlinear Science and Numerical Simulation, 2021

Abstract Lagrangian descriptors introduced a decade ago have revealed as a powerful tool to unvei... more Abstract Lagrangian descriptors introduced a decade ago have revealed as a powerful tool to unveil the intricacies of the phase space of dynamical systems in a very easy way. They have been extensively used to study chaotic motion in a variety of different situations, but much less attention has been paid to applications to the regular regions of phase space. In this paper, we show the potential of this recent mathematical tool, when suitably manipulated, to compute and fully characterize invariant tori of generic systems. To illustrate the method, we present an application to the well known Henon-Heiles Hamiltonian, a paradigmatic example in nonlinear science. In particular, we demonstrate that the Lagrangian descriptors associated with regular orbits oscillate around an asymptotic value when divided over the integration time, which enables the computation of the frequencies characterizing the invariant tori in which regular motion takes place.

Unveiling the chaotic structure in phase space of molecular systems using Lagrangian descriptors

Physical Review E, 2019

We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Ma... more We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Mancho et al., Commun. Nonlinear Sci. Numer. Simul. 18, 3530 (2013)] to unveil the usually rich dynamics taking place in the vibrations of molecular systems, especially if they are floppy. The principal novelty of our work is the inclusion of p norms in the definition of the descriptors in this kind of system, which greatly enhances their power to discern among the different structures existing in the phase space. As an illustration we use the LiCN molecule described by realistic potentials in two and three dimensions, which exhibits chaotic motion within a mixed phase space in the isomerization between the two wells corresponding to the linear isomer stable configurations, LiNC and LiCN. In particular, we pay special attention to the manifolds emerging from the unstable fixed point between the corresponding isomer wells, and also to the marginally stable structures around a parabolic point existing near the LiNC well.

Quantization Scheme for the Experiments with “Walking Droplets”

The Journal of Physical Chemistry A, 2019

In this paper we explore the interest and feasibility of quantizing the macroscopic surface wave ... more In this paper we explore the interest and feasibility of quantizing the macroscopic surface wave generated in the dynamics of walking droplets on a vertically vibrated liquid surface in the limit of high memory of the droplet trajectory, where an astonishing similarity with the quantum behavior has been experimentally observed.

Role of short periodic orbits in quantum maps with continuous openings

Physical review. E, 2018

We apply a recently developed semiclassical theory of short periodic orbits to the continuously o... more We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map-a cantor set given by a region of exactly zero reflectivity-prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for steplike functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case. In order to give a more realistic interpretation of these results we compare with a Fresnel-type reflectiv...

Scar Functions, Barriers for Chemical Reactivity, and Vibrational Basis Sets

The Journal of Physical Chemistry A, 2016

The performance of a recently proposed method to efficiently calculate scar functions is analyzed... more The performance of a recently proposed method to efficiently calculate scar functions is analyzed in problems of chemical interest. An application to the computation of wave functions associated with barriers relevant for the LiNC=LiCN isomerization reaction is presented as an illustration. These scar functions also constitute excellent elements for basis sets suitable for quantum calculation of vibrational energy levels. To illustrate this efficiency a calculation of the LiNC/LiCN eigenfunctions is also presented.

Towards AC-induced optimum control of dynamical localization

EPL (Europhysics Letters), 2015

PACS 05.45.Mt-Quantum chaos; semiclassical methods PACS 42.50.Wk-Mechanical effects of light on m... more PACS 05.45.Mt-Quantum chaos; semiclassical methods PACS 42.50.Wk-Mechanical effects of light on material media, microstructures and particles Abstract-It is shown that dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic modulations having equidistant zeros depends on the impulse transmitted by the external modulation over half-period rather than on the modulation amplitude. This result provides a useful principle for optimally controlling dynamical localization in general periodic systems, which is capable of experimental realization.

$Research paper thumbnail of Causal trajectories description of atom diffraction by surfaces$

Causal trajectories description of atom diffraction by surfaces

Physical Review B, 2000

The method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of ato... more The method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of atom diffraction by surfaces. As an example, a realistic model for the scattering of He off corrugated Cu is considered. In this way, the final angular distribution of trajectories is obtained by box counting, which is in excellent agreement with the results calculated by standard S matrix methods of scattering theory. More interestingly, the accumulation of quantum trajectories at the different diffraction peaks is explained in terms of the corresponding quantum potential. This nonlocal potential ''guides'' the trajectories causing a transition from a distribution near the surface, which reproduces its shape, to the final diffraction pattern observed in the asymptotic region, far from the diffracting object. These two regimes are homologous to the Fresnel and Fraunhofer regions described in undulatory optics. Finally, the turning points of the quantum trajectories provide a better description of the surface electronic density than the corresponding classical ones, usually employed for this task.

Quantum chaos in the de Broglie-Bohm theory

Peer Reviewe

Quantum localization through interference on homoclinic and heteroclinic circuits

New Journal of Physics, 2008

Localization effects due to scarring constitute one of the clearest indications of the relevance ... more Localization effects due to scarring constitute one of the clearest indications of the relevance of interference in the transport of quantum probability density along quantized closed circuits in phase space. The corresponding path can be obvious, such as the scarring periodic orbit (PO) itself which produces time recurrences at multiples of the period. However, there are others more elaborate which

Transition from order to chaos in molecular wave functions and spectra

The Journal of Chemical Physics, 1996

Finite-barrier corrections for multidimensional barriers in colored noise

Physical Review E, 2019

The usual identification of reactive trajectories for the calculation of reaction rates requires ... more The usual identification of reactive trajectories for the calculation of reaction rates requires very timeconsuming simulations, particularly if the environment presents memory effects. In this paper, we develop a method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.

Periodic Orbits and Quantum Mechanics of Molecular Hamiltonian Systems

Hamiltonian Systems with Three or More Degrees of Freedom, 1999

... York. 4. Borondo, F. and Benito, RM (1995) in E. Yurtsever (ed), Frontiers of Chemical Physic... more

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

Physical Review E, 2020

The correlation diagrams of vibrational energy levels considering the Planck constant as a variab... more 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.

Correspondence principle, semiclassical quantization and chaos in the dynamics of triatomic molecules

Irregular many-body dynamics of spinor Bose-Einstein condensates in an optical lattice

Physical Review E, 2008

The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in a... more The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in an optical lattice, where light-induced and static magnetic dipole-dipole interactions originate the interplay of the condensate at each site, are investigated. Classical-quantum correspondence in the large-spin limit is studied. Quantum chaotic features are studied through analysis of the irregular spectrum and time evolution of the Shannon entropy of wave packets. We show how the optical lattice strength influences the system dynamics, and is responsible for a transition from regular to irregular bahavior.

Vortex dynamics and their interactions in quantum trajectories

Journal of Physics A: Mathematical and Theoretical, 2007

Theoretical study of the rotational predissociation of the c 3πu state of H2

Chemical Physics Letters, 1988

Abstract We present a theoretical study of the predissociation of the c 3Πu state of H2. The rota... more Abstract We present a theoretical study of the predissociation of the c 3Πu state of H2. The rotational coupling responsible for this process is accurately calculated for the internuclear distances of interest, and the validity of the pure precession approximation in this particular case is analyzed. Our numerical results for the predissociative lifetimes of the vibrational levels of this state are compared with previous experimental and theoretical values.

Deep learning methods for the computation of vibrational wavefunctions

Communications in Nonlinear Science and Numerical Simulation, 2021

• Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining ... more • Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining good approximations to the corresponding eigenenergies and eigenfunctions. • Modifications of the neural network to make it suitable for obtaining highly excited eigenfunctions, where no obvious nodal patterns exist, and quantum numbers are not well defined. • Application to typical molecular potentials.

Deep learning methods for the computation of vibrational wavefunctions

Communications in Nonlinear Science and Numerical Simulation, 2021

• Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining ... more • Use of deep neural networks to solve the time independent Schrödinger equation, thus obtaining good approximations to the corresponding eigenenergies and eigenfunctions. • Modifications of the neural network to make it suitable for obtaining highly excited eigenfunctions, where no obvious nodal patterns exist, and quantum numbers are not well defined. • Application to typical molecular potentials.

Rate calculation with correlated noise

arXiv: Chaotic Dynamics, 2016

The usual identification of reactive trajectories for the calculation of reaction rates requires ... more The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a new method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.

Lagrangian descriptors and regular motion

Communications in Nonlinear Science and Numerical Simulation, 2021

Abstract Lagrangian descriptors introduced a decade ago have revealed as a powerful tool to unvei... more Abstract Lagrangian descriptors introduced a decade ago have revealed as a powerful tool to unveil the intricacies of the phase space of dynamical systems in a very easy way. They have been extensively used to study chaotic motion in a variety of different situations, but much less attention has been paid to applications to the regular regions of phase space. In this paper, we show the potential of this recent mathematical tool, when suitably manipulated, to compute and fully characterize invariant tori of generic systems. To illustrate the method, we present an application to the well known Henon-Heiles Hamiltonian, a paradigmatic example in nonlinear science. In particular, we demonstrate that the Lagrangian descriptors associated with regular orbits oscillate around an asymptotic value when divided over the integration time, which enables the computation of the frequencies characterizing the invariant tori in which regular motion takes place.

Unveiling the chaotic structure in phase space of molecular systems using Lagrangian descriptors

Physical Review E, 2019

We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Ma... more We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Mancho et al., Commun. Nonlinear Sci. Numer. Simul. 18, 3530 (2013)] to unveil the usually rich dynamics taking place in the vibrations of molecular systems, especially if they are floppy. The principal novelty of our work is the inclusion of p norms in the definition of the descriptors in this kind of system, which greatly enhances their power to discern among the different structures existing in the phase space. As an illustration we use the LiCN molecule described by realistic potentials in two and three dimensions, which exhibits chaotic motion within a mixed phase space in the isomerization between the two wells corresponding to the linear isomer stable configurations, LiNC and LiCN. In particular, we pay special attention to the manifolds emerging from the unstable fixed point between the corresponding isomer wells, and also to the marginally stable structures around a parabolic point existing near the LiNC well.

Quantization Scheme for the Experiments with “Walking Droplets”

The Journal of Physical Chemistry A, 2019

In this paper we explore the interest and feasibility of quantizing the macroscopic surface wave ... more In this paper we explore the interest and feasibility of quantizing the macroscopic surface wave generated in the dynamics of walking droplets on a vertically vibrated liquid surface in the limit of high memory of the droplet trajectory, where an astonishing similarity with the quantum behavior has been experimentally observed.

Role of short periodic orbits in quantum maps with continuous openings

Physical review. E, 2018

We apply a recently developed semiclassical theory of short periodic orbits to the continuously o... more We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map-a cantor set given by a region of exactly zero reflectivity-prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for steplike functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case. In order to give a more realistic interpretation of these results we compare with a Fresnel-type reflectiv...

Scar Functions, Barriers for Chemical Reactivity, and Vibrational Basis Sets

The Journal of Physical Chemistry A, 2016

The performance of a recently proposed method to efficiently calculate scar functions is analyzed... more The performance of a recently proposed method to efficiently calculate scar functions is analyzed in problems of chemical interest. An application to the computation of wave functions associated with barriers relevant for the LiNC=LiCN isomerization reaction is presented as an illustration. These scar functions also constitute excellent elements for basis sets suitable for quantum calculation of vibrational energy levels. To illustrate this efficiency a calculation of the LiNC/LiCN eigenfunctions is also presented.

Towards AC-induced optimum control of dynamical localization

EPL (Europhysics Letters), 2015

PACS 05.45.Mt-Quantum chaos; semiclassical methods PACS 42.50.Wk-Mechanical effects of light on m... more PACS 05.45.Mt-Quantum chaos; semiclassical methods PACS 42.50.Wk-Mechanical effects of light on material media, microstructures and particles Abstract-It is shown that dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic modulations having equidistant zeros depends on the impulse transmitted by the external modulation over half-period rather than on the modulation amplitude. This result provides a useful principle for optimally controlling dynamical localization in general periodic systems, which is capable of experimental realization.

$Research paper thumbnail of Causal trajectories description of atom diffraction by surfaces$

Causal trajectories description of atom diffraction by surfaces

Physical Review B, 2000

The method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of ato... more The method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of atom diffraction by surfaces. As an example, a realistic model for the scattering of He off corrugated Cu is considered. In this way, the final angular distribution of trajectories is obtained by box counting, which is in excellent agreement with the results calculated by standard S matrix methods of scattering theory. More interestingly, the accumulation of quantum trajectories at the different diffraction peaks is explained in terms of the corresponding quantum potential. This nonlocal potential ''guides'' the trajectories causing a transition from a distribution near the surface, which reproduces its shape, to the final diffraction pattern observed in the asymptotic region, far from the diffracting object. These two regimes are homologous to the Fresnel and Fraunhofer regions described in undulatory optics. Finally, the turning points of the quantum trajectories provide a better description of the surface electronic density than the corresponding classical ones, usually employed for this task.

Quantum chaos in the de Broglie-Bohm theory

Peer Reviewe

Quantum localization through interference on homoclinic and heteroclinic circuits

New Journal of Physics, 2008

Localization effects due to scarring constitute one of the clearest indications of the relevance ... more Localization effects due to scarring constitute one of the clearest indications of the relevance of interference in the transport of quantum probability density along quantized closed circuits in phase space. The corresponding path can be obvious, such as the scarring periodic orbit (PO) itself which produces time recurrences at multiples of the period. However, there are others more elaborate which

Transition from order to chaos in molecular wave functions and spectra

The Journal of Chemical Physics, 1996