arXiv subjects

F. J. Arranz

Publications and source records attributed to F. J. Arranz.

7 recordsLinked to original sources

arXiv2026

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.

nlin.CD↗

arXiv2026

Correspondence between classical and quantum resonances

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this 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$\leftrightarrows$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 $\hbar=0$ unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit $\hbar\to0$. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.

nlin.CD↗

arXiv2024

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 non-integrable 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.

nlin.CD↗

arXiv2024

Bifurcations and phase-space structures in KCN molecular system

In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of the potential energy surface. As the energy increases, the phase space combines regions with regular and chaotic motion, a difference that is well captured by the Lagrangian descriptors. We show that the dynamics is mostly governed by the invariant manifolds of the stretch periodic orbits located at the top of one of the energetic barriers of the system. Furthermore, we show a perfect agreement between the bifurcation theory and the differences observed in the phase-space structures as the vibrational energy is modified. The accuracy of our calculations is also assessed by explicit comparison with the invariant manifolds computed using linear dynamics.

nlin.CD↗

arXiv2024

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)] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing Planck constant, we induced a transition from order to chaos, in which scarred wavefunctions 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 novel straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.

nlin.CD↗

arXiv2014

Maximum population transfer in a periodically driven two-level system

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model

quant-ph↗

arXiv2011

The Poincare-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.

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